Geodesic
The even cycle problem for directed graphs
Journal of the American Mathematical Society, Tome 05 (1992) no. 2, pp. 217-229

Voir la notice de l'article provenant de la source American Mathematical Society

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. 
Thomassen, Carsten. The even cycle problem for directed graphs. Journal of the American Mathematical Society, Tome 05 (1992) no. 2, pp. 217-229. doi: 10.1090/S0894-0347-1992-1135027-1
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