de Carvalho, Marcelo H.; Little, C. H. C. Vector spaces and the Petersen graph. (English) Zbl 1180.05085 Electron. J. Comb. 15, No. 1, Research Paper R9, 13 p. (2008). 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. Cited in 1 Document MSC: 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) Keywords:matching covered graph; ear decomposition PDFBibTeX XMLCite \textit{M. H. de Carvalho} and \textit{C. H. C. Little}, Electron. J. Comb. 15, No. 1, Research Paper R9, 13 p. (2008; Zbl 1180.05085) Full Text: EuDML EMIS