Matching and edge-connectivity in regular graphs

Henning and Yeo proved a lower bound for the minimum size of a maximum matching in a connected k -regular graph with n vertices; it is sharp infinitely often. In an earlier paper, we characterized when equality holds. In this paper, we prove a lower bound for the minimum size of a maximum matching in an l -edge-connected k -regular graph with n vertices, for l ≥ 2 and k ≥ 4 . Again it is sharp for infinitely many n , and we characterize when equality holds in the bound.