--- _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. Combinatorica. 2024;44:429-440. doi:10.1007/s00493-023-00078-9 apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2024). Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. Combinatorica, 44, 429–440. https://doi.org/10.1007/s00493-023-00078-9 bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={10.1007/s00493-023-00078-9}, 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.” Combinatorica 44 (2024): 429–40. https://doi.org/10.1007/s00493-023-00078-9.' ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs,” Combinatorica, vol. 44, pp. 429–440, 2024, doi: 10.1007/s00493-023-00078-9.' mla: Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” Combinatorica, vol. 44, Springer Science and Business Media LLC, 2024, pp. 429–40, doi:10.1007/s00493-023-00078-9. 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. arXiv:230508619. Published online 2023. apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Sets of r-graphs that color all r-graphs. In arXiv:2305.08619. 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.” ArXiv:2305.08619, 2023. ieee: Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color all r-graphs,” arXiv:2305.08619. 2023. mla: Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 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. SIAM Journal on Discrete Mathematics. 2023;37(3):1548-1565. doi:10.1137/22m1500654 apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics, 37(3), 1548–1565. https://doi.org/10.1137/22m1500654 bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={10.1137/22m1500654}, number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society for Industrial & 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.” SIAM Journal on Discrete Mathematics 37, no. 3 (2023): 1548–65. https://doi.org/10.1137/22m1500654.' ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs,” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, pp. 1548–1565, 2023, doi: 10.1137/22m1500654.' mla: Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:10.1137/22m1500654. 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: '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. Discrete Applied Mathematics. 2023;337:185-189. doi:10.1016/j.dam.2023.05.008 apa: Steffen, E., & Wolf, I. H. (2023). Bounds for the chromatic index of signed multigraphs. Discrete Applied Mathematics, 337, 185–189. https://doi.org/10.1016/j.dam.2023.05.008 bibtex: '@article{Steffen_Wolf_2023, title={Bounds for the chromatic index of signed multigraphs}, volume={337}, DOI={10.1016/j.dam.2023.05.008}, 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.” Discrete Applied Mathematics 337 (2023): 185–89. https://doi.org/10.1016/j.dam.2023.05.008.' ieee: 'E. Steffen and I. H. Wolf, “Bounds for the chromatic index of signed multigraphs,” Discrete Applied Mathematics, vol. 337, pp. 185–189, 2023, doi: 10.1016/j.dam.2023.05.008.' mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index of Signed Multigraphs.” Discrete Applied Mathematics, vol. 337, Elsevier BV, 2023, pp. 185–89, doi:10.1016/j.dam.2023.05.008. 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. Discrete Mathematics. Published online 2023. doi:10.1016/j.disc.2023.113457 apa: Steffen, E., & Wolf, I. H. (2023). Rotation r-graphs. Discrete Mathematics, Article 113457. https://doi.org/10.1016/j.disc.2023.113457 bibtex: '@article{Steffen_Wolf_2023, title={Rotation r-graphs}, DOI={10.1016/j.disc.2023.113457}, 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.” Discrete Mathematics, 2023. https://doi.org/10.1016/j.disc.2023.113457. ieee: 'E. Steffen and I. H. Wolf, “Rotation r-graphs,” Discrete Mathematics, Art. no. 113457, 2023, doi: 10.1016/j.disc.2023.113457.' mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” Discrete Mathematics, 113457, Elsevier BV, 2023, doi:10.1016/j.disc.2023.113457. 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: '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. Graphs and Combinatorics. 2022;38(3). doi:10.1007/s00373-022-02506-x apa: Steffen, E., & Wolf, I. H. (2022). Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices. Graphs and Combinatorics, 38(3), Article 104. https://doi.org/10.1007/s00373-022-02506-x bibtex: '@article{Steffen_Wolf_2022, title={Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices}, volume={38}, DOI={10.1007/s00373-022-02506-x}, 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.” Graphs and Combinatorics 38, no. 3 (2022). https://doi.org/10.1007/s00373-022-02506-x. ieee: 'E. Steffen and I. H. Wolf, “Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices,” Graphs and Combinatorics, vol. 38, no. 3, Art. no. 104, 2022, doi: 10.1007/s00373-022-02506-x.' mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices.” Graphs and Combinatorics, vol. 38, no. 3, 104, Springer Science and Business Media LLC, 2022, doi:10.1007/s00373-022-02506-x. 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' ...