Closure and factor-critical graphs Original Research Article

A graph G is said to be n-factor-critical if G−T has a perfect matching for each T⊂V(G) with |T|=n. We study the relation between n-factor-criticality and various closure operations, which are usually considered in the theory of hamiltonian graphs. In particular, we give necessary and sufficient conditions for a graph to be n-factor-critical in terms of these closures. We also investigate the relations between the various closures and matching extension.