---
_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: '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: '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: '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'
...