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.
Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs / Ma, Yulai; Mattiolo, Davide; Steffen, Eckhard; Wolf, Isaak H.. - In: COMBINATORICA. - ISSN 0209-9683. - 44:2(2023), pp. 429-440. [10.1007/s00493-023-00078-9]
Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs
Mattiolo, Davide;
2023
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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