Edge-connectivity and pairwise disjoint perfect matchings in regular graphs
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.