k-正则图的可扩性质

The Extendability of K-regular Graph

设 G是 k正则 (k-1) -边连通的简单图 ,F是 G的一个边集且 | F|≤ k-1。本文证明了如下结论 :如果 G有完美匹配 ,则 G-F也有完美匹配。于是 ,我们推出 :如果 G有完美匹配 ,则 G是 1-可扩图。

Let G be an (k-1)-edge connected and k-regular simple graph,and F is an edge set of G with |F|≤k-1.In this paper,we prove that G-F has complete matching if G has a complete matching.Thus we deduce that G is 1-extendable if G has a complete matching.\;