For \(0 \le t \le r\) 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 \(m(t,r) \le r-2\) for all \(t \not = 5\), and \(m(t,r) \le r-3\) if r is even. We prove that \(m(2l,r) \le 3l - 6\) for every \(l \ge 3\) and \(r \ge 2 l\).

中文翻译：

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正则图中的边连通性和成对不相交完美匹配

对于\(0 \le t \le r\)令m ( t ,  r ) 为最大数s，使得每个t边连接的r图具有s成对不相交完美匹配。m ( t ,  r )的值只有几个已知，例如\(m(3,3)=m(4,r)=1\)和\(m(t,r) \le r- 2\)对于所有\(t \not = 5\)，并且\(m(t,r) \le r-3\)如果r是偶数。我们证明对于每个\(l \ge 3\)和\(r \ge 2 l\)都有\(m(2l,r) \le 3l - 6\)。