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