Edge-connectivity and pairwise disjoint perfect matchings in regular graphs

• DOI: 10.48550/arxiv.2208.14835
• Publication Date: 2022-01-01
• Authors: Yulai Ma; Davide Mattiolo; Eckhard Steffen; Isaak H. Wolf
• Keywords: Disjoint sets

For $0 \leq t r$ let $m(t,r)$ be the maximum number $s$ such that every $t$-edge-connected $r$-graph has pairwise disjoint perfect matchings. There are only a few values of known, for instance $m(3,3)=m(4,r)=1$, and $m(t,r) r-2$ all $t \not = 5$, r-3$ if $r$ is even. We prove $m(2l,r) 3l - 6$ $l \geq 3$ $r 2 l$.