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 | References | Similar Articles | Additional Information

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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DOI:
https://doi.org/10.1090/S0894-0347-1992-1135027-1

Article copyright:
© Copyright 1992
American Mathematical Society