Equimatchable Claw-Free Graphs
arXiv:1607.00476 · doi:10.1016/j.disc.2018.06.043
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.