[{"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 \u0003 = 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."}],"status":"public","publication":"Combinatorica","type":"journal_article","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"language":[{"iso":"eng"}],"_id":"49905","department":[{"_id":"542"}],"user_id":"15540","year":"2024","page":"429-440","intvolume":"        44","citation":{"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>.","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>","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.","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} }","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>."},"publication_identifier":{"issn":["0209-9683","1439-6912"]},"publication_status":"published","title":"Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs","doi":"10.1007/s00493-023-00078-9","publisher":"Springer Science and Business Media LLC","date_updated":"2024-03-22T12:11:35Z","volume":44,"author":[{"id":"92748","full_name":"Ma, Yulai","last_name":"Ma","first_name":"Yulai"},{"first_name":"Davide","last_name":"Mattiolo","full_name":"Mattiolo, Davide"},{"orcid":"0000-0002-9808-7401","last_name":"Steffen","id":"15548","full_name":"Steffen, Eckhard","first_name":"Eckhard"},{"last_name":"Wolf","id":"88145","full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus"}],"date_created":"2023-12-20T10:31:27Z"},{"type":"journal_article","publication":"Discrete Applied Mathematics","status":"public","_id":"51351","user_id":"15540","department":[{"_id":"542"}],"keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics"],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0166-218X"]},"year":"2023","citation":{"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>","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.","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} }","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>.","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>.","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>"},"page":"185-189","intvolume":"       337","publisher":"Elsevier BV","date_updated":"2024-02-14T17:33:59Z","author":[{"full_name":"Steffen, Eckhard","id":"15548","last_name":"Steffen","orcid":"0000-0002-9808-7401","first_name":"Eckhard"},{"full_name":"Wolf, Isaak Hieronymus","id":"88145","last_name":"Wolf","first_name":"Isaak Hieronymus"}],"date_created":"2024-02-14T17:33:29Z","volume":337,"title":"Bounds for the chromatic index of signed multigraphs","doi":"10.1016/j.dam.2023.05.008"},{"status":"public","type":"journal_article","publication":"Discrete Mathematics","language":[{"iso":"eng"}],"article_number":"113457","keyword":["Discrete Mathematics and Combinatorics","Theoretical Computer Science"],"user_id":"15540","department":[{"_id":"542"}],"_id":"51357","citation":{"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>.","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>.","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} }","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)."},"year":"2023","publication_status":"published","publication_identifier":{"issn":["0012-365X"]},"doi":"10.1016/j.disc.2023.113457","title":"Rotation r-graphs","author":[{"first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","id":"15548"},{"first_name":"Isaak Hieronymus","id":"88145","full_name":"Wolf, Isaak Hieronymus","last_name":"Wolf"}],"date_created":"2024-02-16T08:44:50Z","date_updated":"2024-02-16T08:45:10Z","publisher":"Elsevier BV"},{"citation":{"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.","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.","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>.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).","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} }","mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” <i>ArXiv:2305.08619</i>, 2023."},"year":"2023","title":"Sets of r-graphs that color all r-graphs","date_created":"2023-05-16T10:07:47Z","author":[{"last_name":"Ma","id":"92748","full_name":"Ma, Yulai","first_name":"Yulai"},{"full_name":"Mattiolo, Davide","last_name":"Mattiolo","first_name":"Davide"},{"first_name":"Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen","id":"15548","full_name":"Steffen, Eckhard"},{"last_name":"Wolf","full_name":"Wolf, Isaak Hieronymus","id":"88145","first_name":"Isaak Hieronymus"}],"date_updated":"2023-05-16T11:17:26Z","status":"public","type":"preprint","publication":"arXiv:2305.08619","language":[{"iso":"eng"}],"user_id":"15540","department":[{"_id":"542"}],"_id":"44859","external_id":{"arxiv":["2305.08619"]}},{"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"_id":"46256","department":[{"_id":"542"}],"user_id":"15540","status":"public","publication":"SIAM Journal on Discrete Mathematics","type":"journal_article","title":"Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs","doi":"10.1137/22m1500654","publisher":"Society for Industrial & Applied Mathematics (SIAM)","date_updated":"2023-08-01T10:09:35Z","volume":37,"date_created":"2023-08-01T10:08:32Z","author":[{"id":"92748","full_name":"Ma, Yulai","last_name":"Ma","first_name":"Yulai"},{"first_name":"Davide","last_name":"Mattiolo","full_name":"Mattiolo, Davide"},{"first_name":"Eckhard","full_name":"Steffen, Eckhard","id":"15548","last_name":"Steffen","orcid":"0000-0002-9808-7401"},{"first_name":"Isaak Hieronymus","last_name":"Wolf","id":"88145","full_name":"Wolf, Isaak Hieronymus"}],"year":"2023","page":"1548-1565","intvolume":"        37","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>","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>.","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>.","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} }","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.","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>"},"publication_identifier":{"issn":["0895-4801","1095-7146"]},"publication_status":"published","issue":"3"},{"publisher":"Springer Science and Business Media LLC","date_created":"2022-05-31T06:13:57Z","title":"Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices","issue":"3","year":"2022","external_id":{"arxiv":["2109.11447"]},"keyword":["Discrete Mathematics and Combinatorics","Theoretical Computer Science"],"language":[{"iso":"eng"}],"publication":"Graphs and Combinatorics","date_updated":"2023-05-16T10:41:42Z","author":[{"first_name":"Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen","id":"15548","full_name":"Steffen, Eckhard"},{"last_name":"Wolf","full_name":"Wolf, Isaak Hieronymus","id":"88145","first_name":"Isaak Hieronymus"}],"volume":38,"doi":"10.1007/s00373-022-02506-x","publication_status":"published","publication_identifier":{"issn":["0911-0119","1435-5914"]},"citation":{"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} }","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).","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>","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>","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>.","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>."},"intvolume":"        38","_id":"31543","user_id":"15540","article_number":"104","type":"journal_article","status":"public"}]