  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.
