Equimatchable Claw-Free Graphs
  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. 
Saieed Akbari, Hadi Alizadeh, T{\i}naz Ekim, Didem G\"oz\"upek,   Mordechai Shalom
cs.DM math.CO