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A bi‐subdivision of a graph J is a graph H obtained from J by subdividing each of its edges by inserting an even number of vertices. A matching covered subgraph H of a matching covered graph G is conformal if has a perfect matching. Using the theory of ear decompositions, Lovász (Combinatorica, 3 (1983), 105–117) showed that every nonbipartite matching covered graph has a conformal subgraph...
Ear decompositions of matching covered graphs are important for understanding their structure. By exploiting the properties of the dependence relation introduced by Carvalho and Lucchesi in [2], we are able to provide simple proofs of several well-known theorems concerning ear decompositions. Our method actually provides proofs of generalizations of these theorems. For example, we show that every...
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