Two results on matching extensions with prescribed and proscribed edge sets Original Research Article

Let G be a graph with at least 2(m + n + 1) vertices. Then G is E(m,n) if for each pair of disjoint matchings M,N⊆E(G) of size m and n, respectively, there exists a perfect matching F in G such that M⊆F and F∩N=∅. In this paper, we prove two results concerning the property E(m,n). The first involves the class of claw-free graphs and the second is a result about bipartite graphs.