Ear decompositions of matching covered graphs (Q1125615)

Using the dependence relation introduced by the first two authors, simple proofs are given to several theorems on ear decompositions, for example, that any matching covered graph different from \(K_2\) and \(C_{2n}\) has \(\Delta\)(=maximum degree) edge disjoint removable ears. Every brick different from \(K_4\) and \(\overline{C_6}\) has at least \(\Delta-2\) removable edges. Every nonbipartite matching covered graph has an optimal ear decomposition (i.e., with a minimal number of double ears) which is canonical.