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 graphs 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.

• Type: Journal
• Year: 2011
• Where: EJC
• Authors: Suil O, Douglas B. West
• Keywords: EJC 2011, Information Technology, K-regular Graph, Lower Bound, Minimum Size