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Equimatchable Claw-Free Graphs (1607.00476v3)
Published 2 Jul 2016 in cs.DM and math.CO
Abstract: A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide, to the best of our knowledge, the first characterization of claw-free equimatchable graphs by identifying the equimatchable claw-free graph families. This characterization implies an efficient recognition algorithm.