A note on removable edges in near-bricks

An edge e of a matching covered graph G is removable if $G-e$ is also matching covered. Carvalho, Lucchesi, and Murty showed that every brick G different from K₄ and C₆̄ has at least Δ-2 removable edges, where Δ is the maximum degree of G. In this paper, we generalize the result to irreducible near-bricks, where a graph is irreducible if it contains no single ear of length three or more.