Forbidden pairs for the matching extendability of graphs with connectivity at least 2 or 3.

Let H be a set of connected graphs. A graph G is said to be H -free if G does not contain any member of H as an induced subgraph. A graph G having a perfect matching is called k -extendable if every matching of size k in G can be extended to a perfect matching. In this paper, we characterize the sets H with | H | = 2 such that every (k + 1) -connected H -free graph G of sufficiently large order permitting a perfect matching is k -extendable for k ∈ { 1 , 2 }. [ABSTRACT FROM AUTHOR]