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Vector spaces and the Petersen graph. (English) Zbl 1180.05085

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.

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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