On matching extensions with prescribed and proscribed edge sets II 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 = Ø;. In this paper, we extend previous results due to Chen (Discrete Math., to appear) as well as results of the present authors (Aldred et al., Discrete Math., to appear) concerning the property E(m,n). The first extends a result on claw-free graphs and the second generalizes a result about bipartite graphs.