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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The even cycle problem for directed graphs


Author: Carsten Thomassen
Journal: J. Amer. Math. Soc. 5 (1992), 217-229
MSC: Primary 05C20; Secondary 05C38
MathSciNet review: 1135027
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Abstract: If each arc in a strongly connected directed graph of minimum indegree and outdegree at least 3 is assigned a weight 0 or 1, then the resulting weighted directed graph has a directed cycle of even total weight. This proves a conjecture made by L. Lovász in 1975 and has applications to colour-critical hypergraphs, sign-nonsingular matrices, and permanents of matrices.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0894-0347-1992-1135027-1
PII: S 0894-0347(1992)1135027-1
Article copyright: © Copyright 1992 American Mathematical Society