Geodesic
Vector spaces and the Petersen graph
The electronic journal of combinatorics, Tome 15 (2008)
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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.
DOI : 10.37236/733
Classification : 05C70
Mots-clés : matching covered graph, ear decomposition 
@article{10_37236_733,
     author = {Marcelo H. de Carvalho and C. H. C. Little},
     title = {Vector spaces and the {Petersen} graph},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/733},
     zbl = {1180.05085},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/733/}
}
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Marcelo H. de Carvalho; C. H. C. Little. Vector spaces and the Petersen graph. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/733

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