Degree sum and connectivity conditions for bipartite matching extendable graphs

A graph G is said to be bipartite matching extendable if every matching M which is a perfect matching of an induced bipartite subgraph can be extended to a perfect matching of G.For a graph G,let δ k (G) be the minimum degree sum of an independent set of k vertices,let κ(G) be the connectivity of a graph G.In this paper,we prove that if G is a graph of order 2n with κ(G) ≥ 2 (n/2)+1 and δ 3 (G) ≥ 3 (3n/2)-2,then G is bipartite matching extendable graph.We also show that the bound for the conditions are almost the best possible.