---
_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: '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: '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'
...
---
_id: '32810'
article_number: '103451'
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: Yongtang
  full_name: Shi, Yongtang
  last_name: Shi
- first_name: Weifan
  full_name: Wang, Weifan
  last_name: Wang
- first_name: Yezhou
  full_name: Wu, Yezhou
  last_name: Wu
citation:
  ama: Li J, Ma Y, Shi Y, Wang W, Wu Y. On 3-flow-critical graphs. <i>European Journal
    of Combinatorics</i>. 2021;100. doi:<a href="https://doi.org/10.1016/j.ejc.2021.103451">10.1016/j.ejc.2021.103451</a>
  apa: Li, J., Ma, Y., Shi, Y., Wang, W., &#38; Wu, Y. (2021). On 3-flow-critical
    graphs. <i>European Journal of Combinatorics</i>, <i>100</i>, Article 103451.
    <a href="https://doi.org/10.1016/j.ejc.2021.103451">https://doi.org/10.1016/j.ejc.2021.103451</a>
  bibtex: '@article{Li_Ma_Shi_Wang_Wu_2021, title={On 3-flow-critical graphs}, volume={100},
    DOI={<a href="https://doi.org/10.1016/j.ejc.2021.103451">10.1016/j.ejc.2021.103451</a>},
    number={103451}, journal={European Journal of Combinatorics}, publisher={Elsevier
    BV}, author={Li, Jiaao and Ma, Yulai and Shi, Yongtang and Wang, Weifan and Wu,
    Yezhou}, year={2021} }'
  chicago: Li, Jiaao, Yulai Ma, Yongtang Shi, Weifan Wang, and Yezhou Wu. “On 3-Flow-Critical
    Graphs.” <i>European Journal of Combinatorics</i> 100 (2021). <a href="https://doi.org/10.1016/j.ejc.2021.103451">https://doi.org/10.1016/j.ejc.2021.103451</a>.
  ieee: 'J. Li, Y. Ma, Y. Shi, W. Wang, and Y. Wu, “On 3-flow-critical graphs,” <i>European
    Journal of Combinatorics</i>, vol. 100, Art. no. 103451, 2021, doi: <a href="https://doi.org/10.1016/j.ejc.2021.103451">10.1016/j.ejc.2021.103451</a>.'
  mla: Li, Jiaao, et al. “On 3-Flow-Critical Graphs.” <i>European Journal of Combinatorics</i>,
    vol. 100, 103451, Elsevier BV, 2021, doi:<a href="https://doi.org/10.1016/j.ejc.2021.103451">10.1016/j.ejc.2021.103451</a>.
  short: J. Li, Y. Ma, Y. Shi, W. Wang, Y. Wu, European Journal of Combinatorics 100
    (2021).
date_created: 2022-08-15T09:35:02Z
date_updated: 2022-08-15T09:35:32Z
department:
- _id: '542'
doi: 10.1016/j.ejc.2021.103451
intvolume: '       100'
keyword:
- Discrete Mathematics and Combinatorics
language:
- iso: eng
publication: European Journal of Combinatorics
publication_identifier:
  issn:
  - 0195-6698
publication_status: published
publisher: Elsevier BV
status: public
title: On 3-flow-critical graphs
type: journal_article
user_id: '15540'
volume: 100
year: '2021'
...