Equimatchable factor‐critical graphs

Abstract

Abstract A simple graph G ( X , E ) is factor‐critical if the induced subgraph 〈 X – x 〉 admits a perfect matching for every vertex x of G. It is equimatchable if every maximal matching of G is maximum. The equimatchable non‐factor‐critical graphs have been studied by Lesk, Plummer, and Pulleyblank. In this paper, we study the equimatchable factor‐critical graphs; in particular we show that if such a graph is two‐connected, it is hamiltonian.