A lower bound on the number of removable ears of 1-extendable graphs

Let GG be a 1-extendable graph distinct from K2K2 and C2nC2n. A classical result of Lovász and Plummer (1986) [5, Theorem 5.4.6] states that GG has a removable ear. Carvalho et al. (1999) [3] proved that GG has at least Δ(G)Δ(G) edge-disjoint removable ears, where Δ(G)Δ(G) denotes the maximum degree of GG. In this paper, the authors improve the lower bound and prove that GG has at least m(G)m(G) edge-disjoint removable ears, where m(G)m(G) denotes the minimum number of perfect matchings needed to cover all edges of GG.