Edge-stable equimatchable graphs

BaşlıkEdge-stable equimatchable graphs
Publication TypeJournal Article
Year of Publication2019
AuthorsDeniz, Z., and T. Ekim
JournalDiscrete Applied Mathematics
Anahtar kelimeler1-well-covered, Edge-criticality, Edge-stability, Maximal matching, Shedding vertex

A graph G is equimatchable if every maximal matching of G has the same cardinality. We are interested in equimatchable graphs such that the removal of any edge from the graph preserves the equimatchability. We call an equimatchable graph G edge-stable if G∖e, that is the graph obtained by the removal of edge e from G, is also equimatchable for any e∈E(G). After noticing that edge-stable equimatchable graphs are either 2-connected factor-critical or bipartite, we characterize edge-stable equimatchable graphs. This characterization yields an O(min(n3.376,n1.5m)) time recognition algorithm. Lastly, we introduce and shortly discuss the related notions of edge-critical, vertex-stable and vertex-critical equimatchable graphs. In particular, we emphasize the links between our work and the well-studied notion of shedding vertices, and point out some open questions.