Removable edges in Halin graphs

Abstract

A connected nontrivial graph G is matching covered, if every edge of G is contained in a perfect matching of G. An edge e of a matching covered graph G is removable if G−e is still matching covered. Lovász and Plummer introduced removable edges in connection with ear decompositions of matching covered graphs. By characterizing the structure of removable edges, we obtain that the number of removable edges of Halin graphs G with even number of vertices, other than K4, C6¯ and R8, is at least 14(|V(G)|+2), and the lower bound is attainable.