Edge-connectivity and pairwise disjoint perfect matchings in regular graphs

Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2208.14835 (2022).

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Abstract
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≠5, and m(t,r)≤r−3 if r is even. We prove that m(2l,r)≤3l−6 for every l≥3 and r≥2l.
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arXiv:2208.14835
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Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-connectivity and pairwise disjoint perfect matchings in regular  graphs. arXiv:220814835. Published online 2022.
Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2022). Edge-connectivity and pairwise disjoint perfect matchings in regular  graphs. In arXiv:2208.14835.
@article{Ma_Mattiolo_Steffen_Wolf_2022, title={Edge-connectivity and pairwise disjoint perfect matchings in regular  graphs}, journal={arXiv:2208.14835}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2022} }
Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular  Graphs.” ArXiv:2208.14835, 2022.
Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-connectivity and pairwise disjoint perfect matchings in regular  graphs,” arXiv:2208.14835. 2022.
Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular  Graphs.” ArXiv:2208.14835, 2022.

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