The even cycle problem for directed graphs-Reference-Cited by-同舟云学术

The even cycle problem for directed graphs

Published:1992 Issue:2 Volume:5 Page:217-229
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Thomassen Carsten

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/1992-05-02/S0894-0347-1992-1135027-1/S0894-0347-1992-1135027-1.pdf

Reference17 articles.

1. Cycles of length 0 modulo 𝑘 in directed graphs;Alon, Noga;J. Combin. Theory Ser. B,1989

2. Every 7-regular digraph contains an even cycle;Friedland, Shmuel;J. Combin. Theory Ser. B,1989

3. Graph theory and crystal physics;Kasteleyn, P. W.,1967

4. Signsolvability revisited;Klee, Victor;Linear Algebra Appl.,1984

5. An extension of Kasteleyn’s method of enumerating the 1-factors of planar graphs;Little, Charles H. C.,1974

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