Equimatchable Regular Graphs
Saieed Akbari, Amir Hossein Ghodrati, Mohammad Ali Hosseinzadeh, Ali Iranmanesh · Journal of Graph Theory · 2017
Abstract A graph is called equimatchable if all of its maximal matchings have the same size. Kawarabayashi, Plummer, and Saito showed that the only connected equimatchable 3‐regular graphs are K4 and K3, 3. We extend this result by showing that for an odd positive integer r, if G is a connected equimatchable r‐regular graph, then . Also it is proved that for an even r, a connected triangle‐free equimatchable r‐regular graph is isomorphic to one of the graphs C5, C7, and .