Vector spaces and the Petersen graph (Q1010714)

Summary: It is shown that a matching covered graph has an ear decomposition with no more than one double ear if and only if there is no set \(S\) of edges such that \(|S \cap A|\) is even for every alternating circuit \(A\) but \(|S \cap C|\) is odd for some even circuit \(C\). Two proofs are presented. The first uses vector spaces and the second is constructive. Some applications are also given.