A note on equimatchable graphs

Let G = (V, E) be a graph. A set M of edges is called a matching in G if each vertex in G belongs to at most one edge from M , and M is a maximal matching if any edgeset M ′, such that M ⊂ M ′, is not a matching in G. If all maximal matchings in G have the same cardinality then G is an equimatchable graph. In this paper we characterize the equimatchable graphs of girth at least five. As a consequence we also determine those graphs of girth five or more in which every minimal set of edges dominating edges is minimum. 186 A. FRENDRUP, B. HARTNELL AND P.D. VESTERGAARD