DOIAbstract
AbstractThe stability number of a graph G, denoted by α(G), is the cardinality of a stable set of maximum size in G. If α(G-e)>α(G), then e is an α-critical edge, and if μ(G-e)<μ(G), then e is a μ-critical edge, where μ(G) is the cardinality of a maximum matching in G. G is a König–Egerváry graph if its order equals α(G)+μ(G). Beineke, Harary and Plummer have shown that the set of α-critical edges of a bipartite graph forms a matching. In this paper we generalize this statement to König–Egerváry graphs. We also prove that in a König–Egerváry graph α-critical edges are also μ-critical, and that they coincide in bipartite graphs. For König–Egerváry graphs, we characterize μ-critical edges that are also α-critical. Eventually, we deduce that α...
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