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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 C₆ has at least -2 removable edges, where 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.
Wu et al. (Wed,) studied this question.