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Removable edges in cubic matching covered graphs
An edge $e$ in a matching covered graph $G$ is removable if $G-e$ is matching covered, which was introduced by Lovász and Plummer in connection with ear decompositions of matching covered graphs. A brick is a non-bipartite matching covered graph without non-trivial tight cuts. The importance of bricks stems from the fact that they are building blocks of matching covered graphs. Carvalho et al. [Ear decompositions of matching covered graphs, Combinatorica, 19(2):151-174, 1999] showed that eachdoi:10.48550/arxiv.2202.04279 fatcat:gfopil6dbvep7fw2sskyv7msea