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

Let G be a 1-extendable graph distinct from K 2 and C 2 n . A classical result of Lovász and Plummer (1986) [5, Theorem 5.4.6] states that G has a removable ear. Carvalho et al. (1999) [3] proved that G has at least Δ ( G ) edge-disjoint removable ears, where Δ ( G ) denotes the maximum degree of G . In this paper, the authors improve the lower bound and prove that G has at least m ( G ) edge-disjoint removable ears, where m ( G ) denotes the minimum number of perfect matchings needed to cover all edges of G .