Equimatchable factor‐critical graphs
Odile Favaron · Journal of Graph Theory · 1986
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.