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 kk-regular graph with nn 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 ll-edge-connected kk-regular graph with nn vertices, for l≥2l≥2 and k≥4k≥4. Again it is sharp for infinitely many nn, and we characterize when equality holds in the bound.