مشخصات پژوهش

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 G ∈ {Kr+1, Kr,r}. 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 Kr,r.