Characterization of Equimatchable Even-Regular Graphs

Abstract

The study of equimatchable graphs traces back to Sumner (1979), followed by the foundational work of Lesk, Plummer, and Pulleyblank in 1984. Regarding the characterization of equimatchable regular graphs, Akbari et al. and Eiben et al. have characterized almost all such graphs, leaving the class of odd-order equimatchable $r$-regular graphs with independence number at least $3$ and even $r\ge 6$ unclassified. In the present paper, we give a complete structural characterization of graphs in this remaining class.

29 Pages and 10 figures