---
_id: '59806'
abstract:
- lang: eng
  text: We introduce a model of information dissemination in signed networks. It is
    a discrete-time process in which uninformed actors incrementally receive information
    from their informed neighbors or from the outside. Our goal is to minimize the
    number of confused actors — that is, the number of actors who receive contradictory
    information. We prove upper bounds for the number of confused actors in signed
    networks and in equivalence classes of signed networks. In particular, we show
    that there are signed networks where, for any information placement strategy,
    almost 60% of the actors are confused. Furthermore, this is also the case when
    considering the minimum number of confused actors within an equivalence class
    of signed graphs.
author:
- first_name: Ligang
  full_name: Jin, Ligang
  last_name: Jin
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
citation:
  ama: Jin L, Steffen E. Information dissemination and confusion in signed networks.
    <i>Discrete Applied Mathematics</i>. 2025;373:99-106. doi:<a href="https://doi.org/10.1016/j.dam.2025.04.049">10.1016/j.dam.2025.04.049</a>
  apa: Jin, L., &#38; Steffen, E. (2025). Information dissemination and confusion
    in signed networks. <i>Discrete Applied Mathematics</i>, <i>373</i>, 99–106. <a
    href="https://doi.org/10.1016/j.dam.2025.04.049">https://doi.org/10.1016/j.dam.2025.04.049</a>
  bibtex: '@article{Jin_Steffen_2025, title={Information dissemination and confusion
    in signed networks}, volume={373}, DOI={<a href="https://doi.org/10.1016/j.dam.2025.04.049">10.1016/j.dam.2025.04.049</a>},
    journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Jin,
    Ligang and Steffen, Eckhard}, year={2025}, pages={99–106} }'
  chicago: 'Jin, Ligang, and Eckhard Steffen. “Information Dissemination and Confusion
    in Signed Networks.” <i>Discrete Applied Mathematics</i> 373 (2025): 99–106. <a
    href="https://doi.org/10.1016/j.dam.2025.04.049">https://doi.org/10.1016/j.dam.2025.04.049</a>.'
  ieee: 'L. Jin and E. Steffen, “Information dissemination and confusion in signed
    networks,” <i>Discrete Applied Mathematics</i>, vol. 373, pp. 99–106, 2025, doi:
    <a href="https://doi.org/10.1016/j.dam.2025.04.049">10.1016/j.dam.2025.04.049</a>.'
  mla: Jin, Ligang, and Eckhard Steffen. “Information Dissemination and Confusion
    in Signed Networks.” <i>Discrete Applied Mathematics</i>, vol. 373, Elsevier BV,
    2025, pp. 99–106, doi:<a href="https://doi.org/10.1016/j.dam.2025.04.049">10.1016/j.dam.2025.04.049</a>.
  short: L. Jin, E. Steffen, Discrete Applied Mathematics 373 (2025) 99–106.
date_created: 2025-05-06T07:38:49Z
date_updated: 2025-05-06T07:39:58Z
department:
- _id: '542'
doi: 10.1016/j.dam.2025.04.049
intvolume: '       373'
language:
- iso: eng
page: 99-106
publication: Discrete Applied Mathematics
publication_identifier:
  issn:
  - 0166-218X
publication_status: published
publisher: Elsevier BV
status: public
title: Information dissemination and confusion in signed networks
type: journal_article
user_id: '15540'
volume: 373
year: '2025'
...
---
_id: '59169'
abstract:
- lang: eng
  text: An r-regular graph is an r-graph, if every odd set of vertices is connected
    to its complement by at least r edges. Let G and H be r-graphs. An H-coloring
    of G is a mapping such that each r adjacent edges of G are mapped to r adjacent
    edges of H. For every , let be an inclusion-wise minimal set of connected r-graphs,
    such that for every connected r-graph G there is an which colors G. The Petersen
    Coloring Conjecture states that consists of the Petersen graph P. We show that
    if true, then this is a very exclusive situation. Our main result is that either
    or is an infinite set and if , then is an infinite set. In particular, for all
    , is unique. We first characterize and then prove that if contains more than one
    element, then it is an infinite set. To obtain our main result we show that contains
    the smallest r-graphs of class 2 and the smallest poorly matchable r-graphs, and
    we determine the smallest r-graphs of class 2.
article_number: '16'
author:
- first_name: Yulai
  full_name: Ma, Yulai
  last_name: Ma
- first_name: Davide
  full_name: Mattiolo, Davide
  last_name: Mattiolo
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak H.
  full_name: Wolf, Isaak H.
  last_name: Wolf
citation:
  ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-Graphs that Color All r-Graphs.
    <i>Combinatorica</i>. 2025;45(2). doi:<a href="https://doi.org/10.1007/s00493-025-00144-4">10.1007/s00493-025-00144-4</a>
  apa: Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2025). Sets of r-Graphs
    that Color All r-Graphs. <i>Combinatorica</i>, <i>45</i>(2), Article 16. <a href="https://doi.org/10.1007/s00493-025-00144-4">https://doi.org/10.1007/s00493-025-00144-4</a>
  bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2025, title={Sets of r-Graphs that Color
    All r-Graphs}, volume={45}, DOI={<a href="https://doi.org/10.1007/s00493-025-00144-4">10.1007/s00493-025-00144-4</a>},
    number={216}, journal={Combinatorica}, publisher={Springer Science and Business
    Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf,
    Isaak H.}, year={2025} }'
  chicago: Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak H. Wolf. “Sets of
    R-Graphs That Color All r-Graphs.” <i>Combinatorica</i> 45, no. 2 (2025). <a href="https://doi.org/10.1007/s00493-025-00144-4">https://doi.org/10.1007/s00493-025-00144-4</a>.
  ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-Graphs that Color
    All r-Graphs,” <i>Combinatorica</i>, vol. 45, no. 2, Art. no. 16, 2025, doi: <a
    href="https://doi.org/10.1007/s00493-025-00144-4">10.1007/s00493-025-00144-4</a>.'
  mla: Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” <i>Combinatorica</i>,
    vol. 45, no. 2, 16, Springer Science and Business Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s00493-025-00144-4">10.1007/s00493-025-00144-4</a>.
  short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 45 (2025).
date_created: 2025-03-27T09:46:34Z
date_updated: 2025-03-27T09:48:48Z
department:
- _id: '542'
doi: 10.1007/s00493-025-00144-4
intvolume: '        45'
issue: '2'
language:
- iso: eng
publication: Combinatorica
publication_identifier:
  issn:
  - 0209-9683
  - 1439-6912
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Sets of r-Graphs that Color All r-Graphs
type: journal_article
user_id: '15540'
volume: 45
year: '2025'
...
---
_id: '61042'
abstract:
- lang: eng
  text: We introduce the concept of a k-token signed graph and study some of its combinatorial
    and algebraic properties. We prove that two switching isomorphic signed graphs
    have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum
    of a balanced signed graph is contained in the Laplacian spectra of its k-token
    signed graph. Besides, we introduce and study the unbalance level of a signed
    graph, which is a new parameter that measures how far a signed graph is from being
    balanced. Moreover, we study the relation between the frustration index and the
    unbalance level of signed graphs and their token signed graphs.
article_number: '7'
author:
- first_name: C.
  full_name: Dalfó, C.
  last_name: Dalfó
- first_name: M. A.
  full_name: Fiol, M. A.
  last_name: Fiol
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
citation:
  ama: Dalfó C, Fiol MA, Steffen E. On token signed graphs. <i>Journal of Algebraic
    Combinatorics</i>. 2025;62(1). doi:<a href="https://doi.org/10.1007/s10801-025-01416-4">10.1007/s10801-025-01416-4</a>
  apa: Dalfó, C., Fiol, M. A., &#38; Steffen, E. (2025). On token signed graphs. <i>Journal
    of Algebraic Combinatorics</i>, <i>62</i>(1), Article 7. <a href="https://doi.org/10.1007/s10801-025-01416-4">https://doi.org/10.1007/s10801-025-01416-4</a>
  bibtex: '@article{Dalfó_Fiol_Steffen_2025, title={On token signed graphs}, volume={62},
    DOI={<a href="https://doi.org/10.1007/s10801-025-01416-4">10.1007/s10801-025-01416-4</a>},
    number={17}, journal={Journal of Algebraic Combinatorics}, publisher={Springer
    Science and Business Media LLC}, author={Dalfó, C. and Fiol, M. A. and Steffen,
    Eckhard}, year={2025} }'
  chicago: Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” <i>Journal
    of Algebraic Combinatorics</i> 62, no. 1 (2025). <a href="https://doi.org/10.1007/s10801-025-01416-4">https://doi.org/10.1007/s10801-025-01416-4</a>.
  ieee: 'C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” <i>Journal
    of Algebraic Combinatorics</i>, vol. 62, no. 1, Art. no. 7, 2025, doi: <a href="https://doi.org/10.1007/s10801-025-01416-4">10.1007/s10801-025-01416-4</a>.'
  mla: Dalfó, C., et al. “On Token Signed Graphs.” <i>Journal of Algebraic Combinatorics</i>,
    vol. 62, no. 1, 7, Springer Science and Business Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s10801-025-01416-4">10.1007/s10801-025-01416-4</a>.
  short: C. Dalfó, M.A. Fiol, E. Steffen, Journal of Algebraic Combinatorics 62 (2025).
date_created: 2025-08-28T07:50:03Z
date_updated: 2025-08-28T07:57:27Z
department:
- _id: '542'
doi: 10.1007/s10801-025-01416-4
intvolume: '        62'
issue: '1'
language:
- iso: eng
publication: Journal of Algebraic Combinatorics
publication_identifier:
  issn:
  - 0925-9899
  - 1572-9192
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On token signed graphs
type: journal_article
user_id: '15540'
volume: 62
year: '2025'
...
---
_id: '63187'
author:
- first_name: Arnott Jeffery Joel
  full_name: Kidner, Arnott Jeffery Joel
  id: '111755'
  last_name: Kidner
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Weiqiang
  full_name: Yu, Weiqiang
  id: '117508'
  last_name: Yu
citation:
  ama: Kidner AJJ, Steffen E, Yu W. Edge-coloring 4- and 5-regular projective planar
    graphs with no Petersen-minor. <i>arXiv:251214285</i>. Published online 2025.
  apa: Kidner, A. J. J., Steffen, E., &#38; Yu, W. (2025). Edge-coloring 4- and 5-regular
    projective planar graphs with no Petersen-minor. In <i>arXiv:2512.14285</i>.
  bibtex: '@article{Kidner_Steffen_Yu_2025, title={Edge-coloring 4- and 5-regular
    projective planar graphs with no Petersen-minor}, journal={arXiv:2512.14285},
    author={Kidner, Arnott Jeffery Joel and Steffen, Eckhard and Yu, Weiqiang}, year={2025}
    }'
  chicago: Kidner, Arnott Jeffery Joel, Eckhard Steffen, and Weiqiang Yu. “Edge-Coloring
    4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>,
    2025.
  ieee: A. J. J. Kidner, E. Steffen, and W. Yu, “Edge-coloring 4- and 5-regular projective
    planar graphs with no Petersen-minor,” <i>arXiv:2512.14285</i>. 2025.
  mla: Kidner, Arnott Jeffery Joel, et al. “Edge-Coloring 4- and 5-Regular Projective
    Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>, 2025.
  short: A.J.J. Kidner, E. Steffen, W. Yu, ArXiv:2512.14285 (2025).
date_created: 2025-12-17T14:40:23Z
date_updated: 2025-12-18T13:17:18Z
department:
- _id: '542'
external_id:
  arxiv:
  - '2512.14285'
language:
- iso: eng
publication: arXiv:2512.14285
status: public
title: Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor
type: preprint
user_id: '15540'
year: '2025'
...
---
_id: '49905'
abstract:
- lang: eng
  text: "For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected
    r-graph has s pairwise disjoint perfect matchings. There are only a few values
    of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for
    all t \x03 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤
    3l − 6 for every l ≥ 3 and r ≥ 2l."
author:
- first_name: Yulai
  full_name: Ma, Yulai
  id: '92748'
  last_name: Ma
- first_name: Davide
  full_name: Mattiolo, Davide
  last_name: Mattiolo
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
  full_name: Wolf, Isaak Hieronymus
  id: '88145'
  last_name: Wolf
citation:
  ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint
    Perfect Matchings in Regular Graphs. <i>Combinatorica</i>. 2024;44:429-440. doi:<a
    href="https://doi.org/10.1007/s00493-023-00078-9">10.1007/s00493-023-00078-9</a>
  apa: Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2024). Edge-Connectivity
    and Pairwise Disjoint Perfect Matchings in Regular Graphs. <i>Combinatorica</i>,
    <i>44</i>, 429–440. <a href="https://doi.org/10.1007/s00493-023-00078-9">https://doi.org/10.1007/s00493-023-00078-9</a>
  bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise
    Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={<a href="https://doi.org/10.1007/s00493-023-00078-9">10.1007/s00493-023-00078-9</a>},
    journal={Combinatorica}, publisher={Springer Science and Business Media LLC},
    author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus},
    year={2024}, pages={429–440} }'
  chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
    “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.”
    <i>Combinatorica</i> 44 (2024): 429–40. <a href="https://doi.org/10.1007/s00493-023-00078-9">https://doi.org/10.1007/s00493-023-00078-9</a>.'
  ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise
    Disjoint Perfect Matchings in Regular Graphs,” <i>Combinatorica</i>, vol. 44,
    pp. 429–440, 2024, doi: <a href="https://doi.org/10.1007/s00493-023-00078-9">10.1007/s00493-023-00078-9</a>.'
  mla: Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings
    in Regular Graphs.” <i>Combinatorica</i>, vol. 44, Springer Science and Business
    Media LLC, 2024, pp. 429–40, doi:<a href="https://doi.org/10.1007/s00493-023-00078-9">10.1007/s00493-023-00078-9</a>.
  short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.
date_created: 2023-12-20T10:31:27Z
date_updated: 2024-03-22T12:11:35Z
department:
- _id: '542'
doi: 10.1007/s00493-023-00078-9
intvolume: '        44'
keyword:
- Computational Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 429-440
publication: Combinatorica
publication_identifier:
  issn:
  - 0209-9683
  - 1439-6912
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs
type: journal_article
user_id: '15540'
volume: 44
year: '2024'
...
---
_id: '56497'
article_number: '114258'
author:
- first_name: Chiara
  full_name: Cappello, Chiara
  last_name: Cappello
- first_name: Reza
  full_name: Naserasr, Reza
  last_name: Naserasr
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Zhouningxin
  full_name: Wang, Zhouningxin
  last_name: Wang
citation:
  ama: Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs.
    <i>Discrete Mathematics</i>. 2024;348(1). doi:<a href="https://doi.org/10.1016/j.disc.2024.114258">10.1016/j.disc.2024.114258</a>
  apa: Cappello, C., Naserasr, R., Steffen, E., &#38; Wang, Z. (2024). Critically
    3-frustrated signed graphs. <i>Discrete Mathematics</i>, <i>348</i>(1), Article
    114258. <a href="https://doi.org/10.1016/j.disc.2024.114258">https://doi.org/10.1016/j.disc.2024.114258</a>
  bibtex: '@article{Cappello_Naserasr_Steffen_Wang_2024, title={Critically 3-frustrated
    signed graphs}, volume={348}, DOI={<a href="https://doi.org/10.1016/j.disc.2024.114258">10.1016/j.disc.2024.114258</a>},
    number={1114258}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Cappello,
    Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2024}
    }'
  chicago: Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang.
    “Critically 3-Frustrated Signed Graphs.” <i>Discrete Mathematics</i> 348, no.
    1 (2024). <a href="https://doi.org/10.1016/j.disc.2024.114258">https://doi.org/10.1016/j.disc.2024.114258</a>.
  ieee: 'C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated
    signed graphs,” <i>Discrete Mathematics</i>, vol. 348, no. 1, Art. no. 114258,
    2024, doi: <a href="https://doi.org/10.1016/j.disc.2024.114258">10.1016/j.disc.2024.114258</a>.'
  mla: Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” <i>Discrete
    Mathematics</i>, vol. 348, no. 1, 114258, Elsevier BV, 2024, doi:<a href="https://doi.org/10.1016/j.disc.2024.114258">10.1016/j.disc.2024.114258</a>.
  short: C. Cappello, R. Naserasr, E. Steffen, Z. Wang, Discrete Mathematics 348 (2024).
date_created: 2024-10-10T12:27:11Z
date_updated: 2024-10-10T12:28:13Z
department:
- _id: '542'
doi: 10.1016/j.disc.2024.114258
intvolume: '       348'
issue: '1'
language:
- iso: eng
publication: Discrete Mathematics
publication_identifier:
  issn:
  - 0012-365X
publication_status: published
publisher: Elsevier BV
status: public
title: Critically 3-frustrated signed graphs
type: journal_article
user_id: '15540'
volume: 348
year: '2024'
...
---
_id: '51351'
author:
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
  full_name: Wolf, Isaak Hieronymus
  id: '88145'
  last_name: Wolf
citation:
  ama: Steffen E, Wolf IH. Bounds for the chromatic index of signed multigraphs. <i>Discrete
    Applied Mathematics</i>. 2023;337:185-189. doi:<a href="https://doi.org/10.1016/j.dam.2023.05.008">10.1016/j.dam.2023.05.008</a>
  apa: Steffen, E., &#38; Wolf, I. H. (2023). Bounds for the chromatic index of signed
    multigraphs. <i>Discrete Applied Mathematics</i>, <i>337</i>, 185–189. <a href="https://doi.org/10.1016/j.dam.2023.05.008">https://doi.org/10.1016/j.dam.2023.05.008</a>
  bibtex: '@article{Steffen_Wolf_2023, title={Bounds for the chromatic index of signed
    multigraphs}, volume={337}, DOI={<a href="https://doi.org/10.1016/j.dam.2023.05.008">10.1016/j.dam.2023.05.008</a>},
    journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Steffen,
    Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={185–189} }'
  chicago: 'Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic
    Index of Signed Multigraphs.” <i>Discrete Applied Mathematics</i> 337 (2023):
    185–89. <a href="https://doi.org/10.1016/j.dam.2023.05.008">https://doi.org/10.1016/j.dam.2023.05.008</a>.'
  ieee: 'E. Steffen and I. H. Wolf, “Bounds for the chromatic index of signed multigraphs,”
    <i>Discrete Applied Mathematics</i>, vol. 337, pp. 185–189, 2023, doi: <a href="https://doi.org/10.1016/j.dam.2023.05.008">10.1016/j.dam.2023.05.008</a>.'
  mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index
    of Signed Multigraphs.” <i>Discrete Applied Mathematics</i>, vol. 337, Elsevier
    BV, 2023, pp. 185–89, doi:<a href="https://doi.org/10.1016/j.dam.2023.05.008">10.1016/j.dam.2023.05.008</a>.
  short: E. Steffen, I.H. Wolf, Discrete Applied Mathematics 337 (2023) 185–189.
date_created: 2024-02-14T17:33:29Z
date_updated: 2024-02-14T17:33:59Z
department:
- _id: '542'
doi: 10.1016/j.dam.2023.05.008
intvolume: '       337'
keyword:
- Applied Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 185-189
publication: Discrete Applied Mathematics
publication_identifier:
  issn:
  - 0166-218X
publication_status: published
publisher: Elsevier BV
status: public
title: Bounds for the chromatic index of signed multigraphs
type: journal_article
user_id: '15540'
volume: 337
year: '2023'
...
---
_id: '45190'
author:
- first_name: Chiara
  full_name: Cappello, Chiara
  id: '72874'
  last_name: Cappello
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
citation:
  ama: 'Cappello C, Steffen E. Graph-Theoretical Models for the Analysis and Design
    of Socio-Technical Networks. In: <i>The Digital Twin of Humans</i>. Springer International
    Publishing; 2023:93--110. doi:<a href="https://doi.org/10.1007/978-3-031-26104-6_5">10.1007/978-3-031-26104-6_5</a>'
  apa: Cappello, C., &#38; Steffen, E. (2023). Graph-Theoretical Models for the Analysis
    and Design of Socio-Technical Networks. In <i>The Digital Twin of Humans</i> (pp.
    93--110). Springer International Publishing. <a href="https://doi.org/10.1007/978-3-031-26104-6_5">https://doi.org/10.1007/978-3-031-26104-6_5</a>
  bibtex: '@inbook{Cappello_Steffen_2023, place={Cham}, title={Graph-Theoretical Models
    for the Analysis and Design of Socio-Technical Networks}, DOI={<a href="https://doi.org/10.1007/978-3-031-26104-6_5">10.1007/978-3-031-26104-6_5</a>},
    booktitle={The Digital Twin of Humans}, publisher={Springer International Publishing},
    author={Cappello, Chiara and Steffen, Eckhard}, year={2023}, pages={93--110} }'
  chicago: 'Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the
    Analysis and Design of Socio-Technical Networks.” In <i>The Digital Twin of Humans</i>,
    93--110. Cham: Springer International Publishing, 2023. <a href="https://doi.org/10.1007/978-3-031-26104-6_5">https://doi.org/10.1007/978-3-031-26104-6_5</a>.'
  ieee: 'C. Cappello and E. Steffen, “Graph-Theoretical Models for the Analysis and
    Design of Socio-Technical Networks,” in <i>The Digital Twin of Humans</i>, Cham:
    Springer International Publishing, 2023, pp. 93--110.'
  mla: Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis
    and Design of Socio-Technical Networks.” <i>The Digital Twin of Humans</i>, Springer
    International Publishing, 2023, pp. 93--110, doi:<a href="https://doi.org/10.1007/978-3-031-26104-6_5">10.1007/978-3-031-26104-6_5</a>.
  short: 'C. Cappello, E. Steffen, in: The Digital Twin of Humans, Springer International
    Publishing, Cham, 2023, pp. 93--110.'
date_created: 2023-05-22T10:22:21Z
date_updated: 2024-02-16T07:42:38Z
department:
- _id: '542'
doi: 10.1007/978-3-031-26104-6_5
language:
- iso: eng
page: 93--110
place: Cham
publication: The Digital Twin of Humans
publication_identifier:
  isbn:
  - '9783031261039'
  - '9783031261046'
publication_status: published
publisher: Springer International Publishing
status: public
title: Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks
type: book_chapter
user_id: '15540'
year: '2023'
...
---
_id: '51357'
article_number: '113457'
author:
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
  full_name: Wolf, Isaak Hieronymus
  id: '88145'
  last_name: Wolf
citation:
  ama: Steffen E, Wolf IH. Rotation r-graphs. <i>Discrete Mathematics</i>. Published
    online 2023. doi:<a href="https://doi.org/10.1016/j.disc.2023.113457">10.1016/j.disc.2023.113457</a>
  apa: Steffen, E., &#38; Wolf, I. H. (2023). Rotation r-graphs. <i>Discrete Mathematics</i>,
    Article 113457. <a href="https://doi.org/10.1016/j.disc.2023.113457">https://doi.org/10.1016/j.disc.2023.113457</a>
  bibtex: '@article{Steffen_Wolf_2023, title={Rotation r-graphs}, DOI={<a href="https://doi.org/10.1016/j.disc.2023.113457">10.1016/j.disc.2023.113457</a>},
    number={113457}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Steffen,
    Eckhard and Wolf, Isaak Hieronymus}, year={2023} }'
  chicago: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” <i>Discrete
    Mathematics</i>, 2023. <a href="https://doi.org/10.1016/j.disc.2023.113457">https://doi.org/10.1016/j.disc.2023.113457</a>.
  ieee: 'E. Steffen and I. H. Wolf, “Rotation r-graphs,” <i>Discrete Mathematics</i>,
    Art. no. 113457, 2023, doi: <a href="https://doi.org/10.1016/j.disc.2023.113457">10.1016/j.disc.2023.113457</a>.'
  mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” <i>Discrete
    Mathematics</i>, 113457, Elsevier BV, 2023, doi:<a href="https://doi.org/10.1016/j.disc.2023.113457">10.1016/j.disc.2023.113457</a>.
  short: E. Steffen, I.H. Wolf, Discrete Mathematics (2023).
date_created: 2024-02-16T08:44:50Z
date_updated: 2024-02-16T08:45:10Z
department:
- _id: '542'
doi: 10.1016/j.disc.2023.113457
keyword:
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
language:
- iso: eng
publication: Discrete Mathematics
publication_identifier:
  issn:
  - 0012-365X
publication_status: published
publisher: Elsevier BV
status: public
title: Rotation r-graphs
type: journal_article
user_id: '15540'
year: '2023'
...
---
_id: '45110'
author:
- first_name: Iris
  full_name: Gräßler, Iris
  id: '47565'
  last_name: Gräßler
  orcid: 0000-0001-5765-971X
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Günter W.
  full_name: Maier, Günter W.
  last_name: Maier
- first_name: Daniel
  full_name: Roesmann, Daniel
  id: '54680'
  last_name: Roesmann
citation:
  ama: 'Gräßler I, Steffen E, Maier GW, Roesmann D. Introduction—The Digital Twin
    of Humans. In: Gräßler I, Maier GW, Steffen E, Roesmann D, eds. <i>The Digital
    Twin of Humans</i>. Springer International Publishing; 2023:3-10. doi:<a href="https://doi.org/10.1007/978-3-031-26104-6_1">10.1007/978-3-031-26104-6_1</a>'
  apa: Gräßler, I., Steffen, E., Maier, G. W., &#38; Roesmann, D. (2023). Introduction—The
    Digital Twin of Humans. In I. Gräßler, G. W. Maier, E. Steffen, &#38; D. Roesmann
    (Eds.), <i>The Digital Twin of Humans</i> (pp. 3–10). Springer International Publishing.
    <a href="https://doi.org/10.1007/978-3-031-26104-6_1">https://doi.org/10.1007/978-3-031-26104-6_1</a>
  bibtex: '@inbook{Gräßler_Steffen_Maier_Roesmann_2023, place={Cham}, title={Introduction—The
    Digital Twin of Humans}, DOI={<a href="https://doi.org/10.1007/978-3-031-26104-6_1">10.1007/978-3-031-26104-6_1</a>},
    booktitle={The Digital Twin of Humans}, publisher={Springer International Publishing},
    author={Gräßler, Iris and Steffen, Eckhard and Maier, Günter W. and Roesmann,
    Daniel}, editor={Gräßler, Iris and Maier, Günter W. and Steffen, Eckhard and Roesmann,
    Daniel}, year={2023}, pages={3–10} }'
  chicago: 'Gräßler, Iris, Eckhard Steffen, Günter W. Maier, and Daniel Roesmann.
    “Introduction—The Digital Twin of Humans.” In <i>The Digital Twin of Humans</i>,
    edited by Iris Gräßler, Günter W. Maier, Eckhard Steffen, and Daniel Roesmann,
    3–10. Cham: Springer International Publishing, 2023. <a href="https://doi.org/10.1007/978-3-031-26104-6_1">https://doi.org/10.1007/978-3-031-26104-6_1</a>.'
  ieee: 'I. Gräßler, E. Steffen, G. W. Maier, and D. Roesmann, “Introduction—The Digital
    Twin of Humans,” in <i>The Digital Twin of Humans</i>, I. Gräßler, G. W. Maier,
    E. Steffen, and D. Roesmann, Eds. Cham: Springer International Publishing, 2023,
    pp. 3–10.'
  mla: Gräßler, Iris, et al. “Introduction—The Digital Twin of Humans.” <i>The Digital
    Twin of Humans</i>, edited by Iris Gräßler et al., Springer International Publishing,
    2023, pp. 3–10, doi:<a href="https://doi.org/10.1007/978-3-031-26104-6_1">10.1007/978-3-031-26104-6_1</a>.
  short: 'I. Gräßler, E. Steffen, G.W. Maier, D. Roesmann, in: I. Gräßler, G.W. Maier,
    E. Steffen, D. Roesmann (Eds.), The Digital Twin of Humans, Springer International
    Publishing, Cham, 2023, pp. 3–10.'
date_created: 2023-05-18T23:45:04Z
date_updated: 2024-03-25T09:08:11Z
department:
- _id: '152'
doi: 10.1007/978-3-031-26104-6_1
editor:
- first_name: Iris
  full_name: Gräßler, Iris
  last_name: Gräßler
- first_name: Günter W.
  full_name: Maier, Günter W.
  last_name: Maier
- first_name: Eckhard
  full_name: Steffen, Eckhard
  last_name: Steffen
- first_name: Daniel
  full_name: Roesmann, Daniel
  last_name: Roesmann
language:
- iso: eng
page: 3-10
place: Cham
publication: The Digital Twin of Humans
publication_identifier:
  isbn:
  - '9783031261039'
  - '9783031261046'
publication_status: published
publisher: Springer International Publishing
quality_controlled: '1'
related_material:
  link:
  - relation: confirmation
    url: https://link.springer.com/book/10.1007/978-3-031-26104-6
status: public
title: Introduction—The Digital Twin of Humans
type: book_chapter
user_id: '5905'
year: '2023'
...
---
_id: '45191'
alternative_title:
- An Interdisciplinary Concept of Digital Working Environments in Industry 4.0
citation:
  ama: Gräßler I, Maier GW, Steffen E, Roesmann D, eds. <i>The Digital Twin of Humans</i>.
    Springer International Publishing; 2023. doi:<a href="https://doi.org/10.1007/978-3-031-26104-6">10.1007/978-3-031-26104-6</a>
  apa: Gräßler, I., Maier, G. W., Steffen, E., &#38; Roesmann, D. (Eds.). (2023).
    <i>The Digital Twin of Humans</i>. Springer International Publishing. <a href="https://doi.org/10.1007/978-3-031-26104-6">https://doi.org/10.1007/978-3-031-26104-6</a>
  bibtex: '@book{Gräßler_Maier_Steffen_Roesmann_2023, place={Cham}, title={The Digital
    Twin of Humans}, DOI={<a href="https://doi.org/10.1007/978-3-031-26104-6">10.1007/978-3-031-26104-6</a>},
    publisher={Springer International Publishing}, year={2023} }'
  chicago: 'Gräßler, Iris, Günter W. Maier, Eckhard Steffen, and Daniel Roesmann,
    eds. <i>The Digital Twin of Humans</i>. Cham: Springer International Publishing,
    2023. <a href="https://doi.org/10.1007/978-3-031-26104-6">https://doi.org/10.1007/978-3-031-26104-6</a>.'
  ieee: 'I. Gräßler, G. W. Maier, E. Steffen, and D. Roesmann, Eds., <i>The Digital
    Twin of Humans</i>. Cham: Springer International Publishing, 2023.'
  mla: Gräßler, Iris, et al., editors. <i>The Digital Twin of Humans</i>. Springer
    International Publishing, 2023, doi:<a href="https://doi.org/10.1007/978-3-031-26104-6">10.1007/978-3-031-26104-6</a>.
  short: I. Gräßler, G.W. Maier, E. Steffen, D. Roesmann, eds., The Digital Twin of
    Humans, Springer International Publishing, Cham, 2023.
date_created: 2023-05-22T10:24:10Z
date_updated: 2024-03-25T09:07:55Z
department:
- _id: '542'
- _id: '152'
doi: 10.1007/978-3-031-26104-6
editor:
- first_name: Iris
  full_name: Gräßler, Iris
  id: '47565'
  last_name: Gräßler
  orcid: 0000-0001-5765-971X
- first_name: Günter W.
  full_name: Maier, Günter W.
  last_name: Maier
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Daniel
  full_name: Roesmann, Daniel
  id: '54680'
  last_name: Roesmann
language:
- iso: eng
place: Cham
publication_identifier:
  isbn:
  - '9783031261039'
  - '9783031261046'
publication_status: published
publisher: Springer International Publishing
quality_controlled: '1'
status: public
title: The Digital Twin of Humans
type: book_editor
user_id: '5905'
year: '2023'
...
---
_id: '44857'
abstract:
- lang: eng
  text: Ancestral reconstruction is a classic task in comparative genomics. Here,
    we study the genome median problem, a related computational problem which, given
    a set of three or more genomes, asks to find a new genome that minimizes the sum
    of pairwise distances between it and the given genomes. The distance stands for
    the amount of evolution observed at the genome level, for which we determine the
    minimum number of rearrangement operations necessary to transform one genome into
    the other. For almost all rearrangement operations the median problem is NP-hard,
    with the exception of the breakpoint median that can be constructed efficiently
    for multichromosomal circular and mixed genomes. In this work, we study the median
    problem under a restricted rearrangement measure called c4-distance, which is
    closely related to the breakpoint and the DCJ distance. We identify tight bounds
    and decomposers of the c4-median and develop algorithms for its construction,
    one exact ILP-based and three combinatorial heuristics. Subsequently, we perform
    experiments on simulated data sets. Our results suggest that the c4-distance is
    useful for the study the genome median problem, from theoretical and practical
    perspectives.
author:
- first_name: Helmuth O.M.
  full_name: Silva, Helmuth O.M.
  last_name: Silva
- first_name: Diego P.
  full_name: Rubert, Diego P.
  last_name: Rubert
- first_name: Eloi
  full_name: Araujo, Eloi
  last_name: Araujo
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Daniel
  full_name: Doerr, Daniel
  last_name: Doerr
- first_name: Fábio V.
  full_name: Martinez, Fábio V.
  last_name: Martinez
citation:
  ama: Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms
    for the genome median under a restricted measure of rearrangement. <i>RAIRO -
    Operations Research</i>. 2023;57(3):1045-1058. doi:<a href="https://doi.org/10.1051/ro/2023052">10.1051/ro/2023052</a>
  apa: Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., &#38; Martinez,
    F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement.
    <i>RAIRO - Operations Research</i>, <i>57</i>(3), 1045–1058. <a href="https://doi.org/10.1051/ro/2023052">https://doi.org/10.1051/ro/2023052</a>
  bibtex: '@article{Silva_Rubert_Araujo_Steffen_Doerr_Martinez_2023, title={Algorithms
    for the genome median under a restricted measure of rearrangement}, volume={57},
    DOI={<a href="https://doi.org/10.1051/ro/2023052">10.1051/ro/2023052</a>}, number={3},
    journal={RAIRO - Operations Research}, publisher={EDP Sciences}, author={Silva,
    Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr,
    Daniel and Martinez, Fábio V.}, year={2023}, pages={1045–1058} }'
  chicago: 'Silva, Helmuth O.M., Diego P. Rubert, Eloi Araujo, Eckhard Steffen, Daniel
    Doerr, and Fábio V. Martinez. “Algorithms for the Genome Median under a Restricted
    Measure of Rearrangement.” <i>RAIRO - Operations Research</i> 57, no. 3 (2023):
    1045–58. <a href="https://doi.org/10.1051/ro/2023052">https://doi.org/10.1051/ro/2023052</a>.'
  ieee: 'H. O. M. Silva, D. P. Rubert, E. Araujo, E. Steffen, D. Doerr, and F. V.
    Martinez, “Algorithms for the genome median under a restricted measure of rearrangement,”
    <i>RAIRO - Operations Research</i>, vol. 57, no. 3, pp. 1045–1058, 2023, doi:
    <a href="https://doi.org/10.1051/ro/2023052">10.1051/ro/2023052</a>.'
  mla: Silva, Helmuth O. M., et al. “Algorithms for the Genome Median under a Restricted
    Measure of Rearrangement.” <i>RAIRO - Operations Research</i>, vol. 57, no. 3,
    EDP Sciences, 2023, pp. 1045–58, doi:<a href="https://doi.org/10.1051/ro/2023052">10.1051/ro/2023052</a>.
  short: H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez,
    RAIRO - Operations Research 57 (2023) 1045–1058.
date_created: 2023-05-16T08:48:22Z
date_updated: 2023-05-16T08:49:30Z
department:
- _id: '542'
doi: 10.1051/ro/2023052
intvolume: '        57'
issue: '3'
keyword:
- Management Science and Operations Research
- Computer Science Applications
- Theoretical Computer Science
language:
- iso: eng
page: 1045-1058
publication: RAIRO - Operations Research
publication_identifier:
  issn:
  - 0399-0559
  - 2804-7303
publication_status: published
publisher: EDP Sciences
status: public
title: Algorithms for the genome median under a restricted measure of rearrangement
type: journal_article
user_id: '15540'
volume: 57
year: '2023'
...
---
_id: '44859'
author:
- first_name: Yulai
  full_name: Ma, Yulai
  id: '92748'
  last_name: Ma
- first_name: Davide
  full_name: Mattiolo, Davide
  last_name: Mattiolo
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
  full_name: Wolf, Isaak Hieronymus
  id: '88145'
  last_name: Wolf
citation:
  ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-graphs that color all r-graphs.
    <i>arXiv:230508619</i>. Published online 2023.
  apa: Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2023). Sets of r-graphs
    that color all r-graphs. In <i>arXiv:2305.08619</i>.
  bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Sets of r-graphs that color
    all r-graphs}, journal={arXiv:2305.08619}, author={Ma, Yulai and Mattiolo, Davide
    and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }'
  chicago: Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
    “Sets of R-Graphs That Color All r-Graphs.” <i>ArXiv:2305.08619</i>, 2023.
  ieee: Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color
    all r-graphs,” <i>arXiv:2305.08619</i>. 2023.
  mla: Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” <i>ArXiv:2305.08619</i>,
    2023.
  short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).
date_created: 2023-05-16T10:07:47Z
date_updated: 2023-05-16T11:17:26Z
department:
- _id: '542'
external_id:
  arxiv:
  - '2305.08619'
language:
- iso: eng
publication: arXiv:2305.08619
status: public
title: Sets of r-graphs that color all r-graphs
type: preprint
user_id: '15540'
year: '2023'
...
---
_id: '46256'
author:
- first_name: Yulai
  full_name: Ma, Yulai
  id: '92748'
  last_name: Ma
- first_name: Davide
  full_name: Mattiolo, Davide
  last_name: Mattiolo
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
  full_name: Wolf, Isaak Hieronymus
  id: '88145'
  last_name: Wolf
citation:
  ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in
    r-Edge-Connected r-Regular Graphs. <i>SIAM Journal on Discrete Mathematics</i>.
    2023;37(3):1548-1565. doi:<a href="https://doi.org/10.1137/22m1500654">10.1137/22m1500654</a>
  apa: Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2023). Pairwise Disjoint
    Perfect Matchings in r-Edge-Connected r-Regular Graphs. <i>SIAM Journal on Discrete
    Mathematics</i>, <i>37</i>(3), 1548–1565. <a href="https://doi.org/10.1137/22m1500654">https://doi.org/10.1137/22m1500654</a>
  bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect
    Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={<a href="https://doi.org/10.1137/22m1500654">10.1137/22m1500654</a>},
    number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society
    for Industrial &#38; Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo,
    Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565}
    }'
  chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
    “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” <i>SIAM
    Journal on Discrete Mathematics</i> 37, no. 3 (2023): 1548–65. <a href="https://doi.org/10.1137/22m1500654">https://doi.org/10.1137/22m1500654</a>.'
  ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect
    Matchings in r-Edge-Connected r-Regular Graphs,” <i>SIAM Journal on Discrete Mathematics</i>,
    vol. 37, no. 3, pp. 1548–1565, 2023, doi: <a href="https://doi.org/10.1137/22m1500654">10.1137/22m1500654</a>.'
  mla: Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected
    r-Regular Graphs.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 37, no. 3,
    Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:<a
    href="https://doi.org/10.1137/22m1500654">10.1137/22m1500654</a>.
  short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics
    37 (2023) 1548–1565.
date_created: 2023-08-01T10:08:32Z
date_updated: 2023-08-01T10:09:35Z
department:
- _id: '542'
doi: 10.1137/22m1500654
intvolume: '        37'
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
page: 1548-1565
publication: SIAM Journal on Discrete Mathematics
publication_identifier:
  issn:
  - 0895-4801
  - 1095-7146
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs
type: journal_article
user_id: '15540'
volume: 37
year: '2023'
...
---
_id: '33741'
abstract:
- lang: eng
  text: There are many concepts of signed graph coloring which are defined by assigning
    colors to the vertices of the graphs. These concepts usually differ in the number
    of self-inverse colors used. We introduce a unifying concept for this kind of
    coloring by assigning elements from symmetric sets to the vertices of the signed
    graphs. In the first part of the paper, we study colorings with elements from
    symmetric sets where the number of self-inverse elements is fixed. We prove a
    Brooks’-type theorem and upper bounds for the corresponding chromatic numbers
    in terms of the chromatic number of the underlying graph. These results are used
    in the second part where we introduce the symset-chromatic number χsym(G,σ) of
    a signed graph (G,σ). We show that the symset-chromatic number gives the minimum
    partition of a signed graph into independent sets and non-bipartite antibalanced
    subgraphs. In particular, χsym(G,σ)≤χ(G). In the final section we show that these
    colorings can also be formalized as DP-colorings.
author:
- first_name: Chiara
  full_name: Cappello, Chiara
  id: '72874'
  last_name: Cappello
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
citation:
  ama: Cappello C, Steffen E. Symmetric Set Coloring of Signed Graphs. <i>Annals of
    Combinatorics</i>. Published online 2022. doi:<a href="https://doi.org/10.1007/s00026-022-00593-4">10.1007/s00026-022-00593-4</a>
  apa: Cappello, C., &#38; Steffen, E. (2022). Symmetric Set Coloring of Signed Graphs.
    <i>Annals of Combinatorics</i>. <a href="https://doi.org/10.1007/s00026-022-00593-4">https://doi.org/10.1007/s00026-022-00593-4</a>
  bibtex: '@article{Cappello_Steffen_2022, title={Symmetric Set Coloring of Signed
    Graphs}, DOI={<a href="https://doi.org/10.1007/s00026-022-00593-4">10.1007/s00026-022-00593-4</a>},
    journal={Annals of Combinatorics}, publisher={Springer Science and Business Media
    LLC}, author={Cappello, Chiara and Steffen, Eckhard}, year={2022} }'
  chicago: Cappello, Chiara, and Eckhard Steffen. “Symmetric Set Coloring of Signed
    Graphs.” <i>Annals of Combinatorics</i>, 2022. <a href="https://doi.org/10.1007/s00026-022-00593-4">https://doi.org/10.1007/s00026-022-00593-4</a>.
  ieee: 'C. Cappello and E. Steffen, “Symmetric Set Coloring of Signed Graphs,” <i>Annals
    of Combinatorics</i>, 2022, doi: <a href="https://doi.org/10.1007/s00026-022-00593-4">10.1007/s00026-022-00593-4</a>.'
  mla: Cappello, Chiara, and Eckhard Steffen. “Symmetric Set Coloring of Signed Graphs.”
    <i>Annals of Combinatorics</i>, Springer Science and Business Media LLC, 2022,
    doi:<a href="https://doi.org/10.1007/s00026-022-00593-4">10.1007/s00026-022-00593-4</a>.
  short: C. Cappello, E. Steffen, Annals of Combinatorics (2022).
date_created: 2022-10-17T07:54:41Z
date_updated: 2023-05-16T10:37:58Z
department:
- _id: '542'
doi: 10.1007/s00026-022-00593-4
external_id:
  arxiv:
  - '2106.05928'
keyword:
- Discrete Mathematics and Combinatorics
language:
- iso: eng
publication: Annals of Combinatorics
publication_identifier:
  issn:
  - 0218-0006
  - 0219-3094
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Symmetric Set Coloring of Signed Graphs
type: journal_article
user_id: '15540'
year: '2022'
...
---
_id: '31543'
article_number: '104'
author:
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
  full_name: Wolf, Isaak Hieronymus
  id: '88145'
  last_name: Wolf
citation:
  ama: Steffen E, Wolf IH. Even Factors in Edge-Chromatic-Critical Graphs with a Small
    Number of Divalent Vertices. <i>Graphs and Combinatorics</i>. 2022;38(3). doi:<a
    href="https://doi.org/10.1007/s00373-022-02506-x">10.1007/s00373-022-02506-x</a>
  apa: Steffen, E., &#38; Wolf, I. H. (2022). Even Factors in Edge-Chromatic-Critical
    Graphs with a Small Number of Divalent Vertices. <i>Graphs and Combinatorics</i>,
    <i>38</i>(3), Article 104. <a href="https://doi.org/10.1007/s00373-022-02506-x">https://doi.org/10.1007/s00373-022-02506-x</a>
  bibtex: '@article{Steffen_Wolf_2022, title={Even Factors in Edge-Chromatic-Critical
    Graphs with a Small Number of Divalent Vertices}, volume={38}, DOI={<a href="https://doi.org/10.1007/s00373-022-02506-x">10.1007/s00373-022-02506-x</a>},
    number={3104}, journal={Graphs and Combinatorics}, publisher={Springer Science
    and Business Media LLC}, author={Steffen, Eckhard and Wolf, Isaak Hieronymus},
    year={2022} }'
  chicago: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Even Factors in Edge-Chromatic-Critical
    Graphs with a Small Number of Divalent Vertices.” <i>Graphs and Combinatorics</i>
    38, no. 3 (2022). <a href="https://doi.org/10.1007/s00373-022-02506-x">https://doi.org/10.1007/s00373-022-02506-x</a>.
  ieee: 'E. Steffen and I. H. Wolf, “Even Factors in Edge-Chromatic-Critical Graphs
    with a Small Number of Divalent Vertices,” <i>Graphs and Combinatorics</i>, vol.
    38, no. 3, Art. no. 104, 2022, doi: <a href="https://doi.org/10.1007/s00373-022-02506-x">10.1007/s00373-022-02506-x</a>.'
  mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Even Factors in Edge-Chromatic-Critical
    Graphs with a Small Number of Divalent Vertices.” <i>Graphs and Combinatorics</i>,
    vol. 38, no. 3, 104, Springer Science and Business Media LLC, 2022, doi:<a href="https://doi.org/10.1007/s00373-022-02506-x">10.1007/s00373-022-02506-x</a>.
  short: E. Steffen, I.H. Wolf, Graphs and Combinatorics 38 (2022).
date_created: 2022-05-31T06:13:57Z
date_updated: 2023-05-16T10:41:42Z
doi: 10.1007/s00373-022-02506-x
external_id:
  arxiv:
  - '2109.11447'
intvolume: '        38'
issue: '3'
keyword:
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
language:
- iso: eng
publication: Graphs and Combinatorics
publication_identifier:
  issn:
  - 0911-0119
  - 1435-5914
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent
  Vertices
type: journal_article
user_id: '15540'
volume: 38
year: '2022'
...
---
_id: '33950'
author:
- first_name: Chiara
  full_name: Cappello, Chiara
  id: '72874'
  last_name: Cappello
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
citation:
  ama: Cappello C, Steffen E. Frustration-critical signed graphs. <i>Discrete Applied
    Mathematics</i>. 2022;322:183-193. doi:<a href="https://doi.org/10.1016/j.dam.2022.08.010">10.1016/j.dam.2022.08.010</a>
  apa: Cappello, C., &#38; Steffen, E. (2022). Frustration-critical signed graphs.
    <i>Discrete Applied Mathematics</i>, <i>322</i>, 183–193. <a href="https://doi.org/10.1016/j.dam.2022.08.010">https://doi.org/10.1016/j.dam.2022.08.010</a>
  bibtex: '@article{Cappello_Steffen_2022, title={Frustration-critical signed graphs},
    volume={322}, DOI={<a href="https://doi.org/10.1016/j.dam.2022.08.010">10.1016/j.dam.2022.08.010</a>},
    journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Cappello,
    Chiara and Steffen, Eckhard}, year={2022}, pages={183–193} }'
  chicago: 'Cappello, Chiara, and Eckhard Steffen. “Frustration-Critical Signed Graphs.”
    <i>Discrete Applied Mathematics</i> 322 (2022): 183–93. <a href="https://doi.org/10.1016/j.dam.2022.08.010">https://doi.org/10.1016/j.dam.2022.08.010</a>.'
  ieee: 'C. Cappello and E. Steffen, “Frustration-critical signed graphs,” <i>Discrete
    Applied Mathematics</i>, vol. 322, pp. 183–193, 2022, doi: <a href="https://doi.org/10.1016/j.dam.2022.08.010">10.1016/j.dam.2022.08.010</a>.'
  mla: Cappello, Chiara, and Eckhard Steffen. “Frustration-Critical Signed Graphs.”
    <i>Discrete Applied Mathematics</i>, vol. 322, Elsevier BV, 2022, pp. 183–93,
    doi:<a href="https://doi.org/10.1016/j.dam.2022.08.010">10.1016/j.dam.2022.08.010</a>.
  short: C. Cappello, E. Steffen, Discrete Applied Mathematics 322 (2022) 183–193.
date_created: 2022-10-28T06:51:31Z
date_updated: 2023-05-16T10:36:51Z
department:
- _id: '542'
doi: 10.1016/j.dam.2022.08.010
external_id:
  arxiv:
  - '2112.02664'
intvolume: '       322'
keyword:
- Applied Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 183-193
publication: Discrete Applied Mathematics
publication_identifier:
  issn:
  - 0166-218X
publication_status: published
publisher: Elsevier BV
status: public
title: Frustration-critical signed graphs
type: journal_article
user_id: '15540'
volume: 322
year: '2022'
...
---
_id: '26408'
author:
- first_name: Davide
  full_name: Mattiolo, Davide
  last_name: Mattiolo
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
citation:
  ama: Mattiolo D, Steffen E. Edge colorings and circular flows on regular graphs.
    <i>Journal of Graph Theory</i>. 2022;99(3):399-413. doi:<a href="https://doi.org/10.1002/jgt.22746">10.1002/jgt.22746</a>
  apa: Mattiolo, D., &#38; Steffen, E. (2022). Edge colorings and circular flows on
    regular graphs. <i>Journal of Graph Theory</i>, <i>99</i>(3), 399–413. <a href="https://doi.org/10.1002/jgt.22746">https://doi.org/10.1002/jgt.22746</a>
  bibtex: '@article{Mattiolo_Steffen_2022, title={Edge colorings and circular flows
    on regular graphs}, volume={99}, DOI={<a href="https://doi.org/10.1002/jgt.22746">10.1002/jgt.22746</a>},
    number={3}, journal={Journal of Graph Theory}, author={Mattiolo, Davide and Steffen,
    Eckhard}, year={2022}, pages={399–413} }'
  chicago: 'Mattiolo, Davide, and Eckhard Steffen. “Edge Colorings and Circular Flows
    on Regular Graphs.” <i>Journal of Graph Theory</i> 99, no. 3 (2022): 399–413.
    <a href="https://doi.org/10.1002/jgt.22746">https://doi.org/10.1002/jgt.22746</a>.'
  ieee: 'D. Mattiolo and E. Steffen, “Edge colorings and circular flows on regular
    graphs,” <i>Journal of Graph Theory</i>, vol. 99, no. 3, pp. 399–413, 2022, doi:
    <a href="https://doi.org/10.1002/jgt.22746">10.1002/jgt.22746</a>.'
  mla: Mattiolo, Davide, and Eckhard Steffen. “Edge Colorings and Circular Flows on
    Regular Graphs.” <i>Journal of Graph Theory</i>, vol. 99, no. 3, 2022, pp. 399–413,
    doi:<a href="https://doi.org/10.1002/jgt.22746">10.1002/jgt.22746</a>.
  short: D. Mattiolo, E. Steffen, Journal of Graph Theory 99 (2022) 399–413.
date_created: 2021-10-18T12:58:47Z
date_updated: 2023-05-16T10:42:45Z
doi: 10.1002/jgt.22746
external_id:
  arxiv:
  - '2001.02484'
intvolume: '        99'
issue: '3'
language:
- iso: eng
page: 399-413
publication: Journal of Graph Theory
publication_identifier:
  issn:
  - 0364-9024
  - 1097-0118
publication_status: published
status: public
title: Edge colorings and circular flows on regular graphs
type: journal_article
user_id: '15540'
volume: 99
year: '2022'
...
---
_id: '22287'
author:
- first_name: Iris
  full_name: Gräßler, Iris
  id: '47565'
  last_name: Gräßler
  orcid: 0000-0001-5765-971X
- first_name: Daniel
  full_name: Roesmann, Daniel
  id: '54680'
  last_name: Roesmann
- first_name: Chiara
  full_name: Cappello, Chiara
  id: '72874'
  last_name: Cappello
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
citation:
  ama: 'Gräßler I, Roesmann D, Cappello C, Steffen E. Skill-based worker assignment
    in a manual assembly line. In: Lutters E, ed. <i>Procedia CIRP Design</i>. Elsevier;
    2021:433-438. doi:<a href="https://doi.org/10.1016/j.procir.2021.05.100">10.1016/j.procir.2021.05.100</a>'
  apa: Gräßler, I., Roesmann, D., Cappello, C., &#38; Steffen, E. (2021). Skill-based
    worker assignment in a manual assembly line. In E. Lutters (Ed.), <i>Procedia
    CIRP Design</i> (pp. 433–438). Elsevier. <a href="https://doi.org/10.1016/j.procir.2021.05.100">https://doi.org/10.1016/j.procir.2021.05.100</a>
  bibtex: '@inproceedings{Gräßler_Roesmann_Cappello_Steffen_2021, title={Skill-based
    worker assignment in a manual assembly line}, DOI={<a href="https://doi.org/10.1016/j.procir.2021.05.100">10.1016/j.procir.2021.05.100</a>},
    booktitle={Procedia CIRP Design}, publisher={Elsevier}, author={Gräßler, Iris
    and Roesmann, Daniel and Cappello, Chiara and Steffen, Eckhard}, editor={Lutters,
    Eric}, year={2021}, pages={433–438} }'
  chicago: Gräßler, Iris, Daniel Roesmann, Chiara Cappello, and Eckhard Steffen. “Skill-Based
    Worker Assignment in a Manual Assembly Line.” In <i>Procedia CIRP Design</i>,
    edited by Eric Lutters, 433–38. Elsevier, 2021. <a href="https://doi.org/10.1016/j.procir.2021.05.100">https://doi.org/10.1016/j.procir.2021.05.100</a>.
  ieee: 'I. Gräßler, D. Roesmann, C. Cappello, and E. Steffen, “Skill-based worker
    assignment in a manual assembly line,” in <i>Procedia CIRP Design</i>, Enschede,
    2021, pp. 433–438, doi: <a href="https://doi.org/10.1016/j.procir.2021.05.100">10.1016/j.procir.2021.05.100</a>.'
  mla: Gräßler, Iris, et al. “Skill-Based Worker Assignment in a Manual Assembly Line.”
    <i>Procedia CIRP Design</i>, edited by Eric Lutters, Elsevier, 2021, pp. 433–38,
    doi:<a href="https://doi.org/10.1016/j.procir.2021.05.100">10.1016/j.procir.2021.05.100</a>.
  short: 'I. Gräßler, D. Roesmann, C. Cappello, E. Steffen, in: E. Lutters (Ed.),
    Procedia CIRP Design, Elsevier, 2021, pp. 433–438.'
conference:
  end_date: 2021-05-21
  location: Enschede
  name: 31st CIRP Design Conference 2021
  start_date: 2021-05-19
date_created: 2021-06-07T08:52:30Z
date_updated: 2022-01-06T06:55:30Z
department:
- _id: '152'
doi: 10.1016/j.procir.2021.05.100
editor:
- first_name: Eric
  full_name: Lutters, Eric
  last_name: Lutters
language:
- iso: eng
page: 433-438
publication: Procedia CIRP Design
publication_identifier:
  issn:
  - 2212-8271
publication_status: published
publisher: Elsevier
status: public
title: Skill-based worker assignment in a manual assembly line
type: conference
user_id: '77594'
year: '2021'
...
---
_id: '34042'
author:
- first_name: Jiaao
  full_name: Li, Jiaao
  last_name: Li
- first_name: Yulai
  full_name: Ma, Yulai
  id: '92748'
  last_name: Ma
- first_name: Zhengke
  full_name: Miao, Zhengke
  last_name: Miao
- first_name: Yongtang
  full_name: Shi, Yongtang
  last_name: Shi
- first_name: Weifan
  full_name: Wang, Weifan
  last_name: Wang
- first_name: Cun-Quan
  full_name: Zhang, Cun-Quan
  last_name: Zhang
citation:
  ama: Li J, Ma Y, Miao Z, Shi Y, Wang W, Zhang C-Q. Nowhere-zero 3-flows in toroidal
    graphs. <i>Journal of Combinatorial Theory, Series B</i>. 2021;153:61-80. doi:<a
    href="https://doi.org/10.1016/j.jctb.2021.11.001">10.1016/j.jctb.2021.11.001</a>
  apa: Li, J., Ma, Y., Miao, Z., Shi, Y., Wang, W., &#38; Zhang, C.-Q. (2021). Nowhere-zero
    3-flows in toroidal graphs. <i>Journal of Combinatorial Theory, Series B</i>,
    <i>153</i>, 61–80. <a href="https://doi.org/10.1016/j.jctb.2021.11.001">https://doi.org/10.1016/j.jctb.2021.11.001</a>
  bibtex: '@article{Li_Ma_Miao_Shi_Wang_Zhang_2021, title={Nowhere-zero 3-flows in
    toroidal graphs}, volume={153}, DOI={<a href="https://doi.org/10.1016/j.jctb.2021.11.001">10.1016/j.jctb.2021.11.001</a>},
    journal={Journal of Combinatorial Theory, Series B}, publisher={Elsevier BV},
    author={Li, Jiaao and Ma, Yulai and Miao, Zhengke and Shi, Yongtang and Wang,
    Weifan and Zhang, Cun-Quan}, year={2021}, pages={61–80} }'
  chicago: 'Li, Jiaao, Yulai Ma, Zhengke Miao, Yongtang Shi, Weifan Wang, and Cun-Quan
    Zhang. “Nowhere-Zero 3-Flows in Toroidal Graphs.” <i>Journal of Combinatorial
    Theory, Series B</i> 153 (2021): 61–80. <a href="https://doi.org/10.1016/j.jctb.2021.11.001">https://doi.org/10.1016/j.jctb.2021.11.001</a>.'
  ieee: 'J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, and C.-Q. Zhang, “Nowhere-zero 3-flows
    in toroidal graphs,” <i>Journal of Combinatorial Theory, Series B</i>, vol. 153,
    pp. 61–80, 2021, doi: <a href="https://doi.org/10.1016/j.jctb.2021.11.001">10.1016/j.jctb.2021.11.001</a>.'
  mla: Li, Jiaao, et al. “Nowhere-Zero 3-Flows in Toroidal Graphs.” <i>Journal of
    Combinatorial Theory, Series B</i>, vol. 153, Elsevier BV, 2021, pp. 61–80, doi:<a
    href="https://doi.org/10.1016/j.jctb.2021.11.001">10.1016/j.jctb.2021.11.001</a>.
  short: J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, C.-Q. Zhang, Journal of Combinatorial
    Theory, Series B 153 (2021) 61–80.
date_created: 2022-11-09T08:43:55Z
date_updated: 2022-11-09T08:44:37Z
department:
- _id: '542'
doi: 10.1016/j.jctb.2021.11.001
intvolume: '       153'
keyword:
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
language:
- iso: eng
page: 61-80
publication: Journal of Combinatorial Theory, Series B
publication_identifier:
  issn:
  - 0095-8956
publication_status: published
publisher: Elsevier BV
status: public
title: Nowhere-zero 3-flows in toroidal graphs
type: journal_article
user_id: '15540'
volume: 153
year: '2021'
...