A note on equimatchable graphs
Allan Frendrup, Bert L. Hartnell, Preben Dahl Vestergaard · 2010
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, andMis a maximal matching if any edgeset M ′, such that M ⊂ M ′,isnota 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.