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{\bf Marcelo H. de Carvalho and C. H. C. Little}
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{\bf Vector Spaces and the Petersen Graph}
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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.
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