BIPARTITE MATCHING EXTENDABILITY AND TOUGHNESS

Let G be a simple graph containing a perfect matching. G is said to be bipartite matching extendable (BM-extendable) if every matching M which is a perfect matching of an induced bipartite subgraph extends to a perfect matching of G. In this paper, we study some relations between toughness and BM-extendability of a graph, including some sufficient or necessary conditions about toughness for a graph to be BM-extendable, and a sufficient condition for a BM-extendable graph to be 1-tough.