Comptes Rendus
Logic
Antidirected paths in 5-chromatic digraphs
Comptes Rendus. Mathématique, Volume 339 (2004) no. 5, pp. 317-320.

Let T5 be the regular 5-tournament. B. Grünbaum proved that T5 is the only 5-tournament which contains no copy of the antidirected path P4. In this Note, we prove that, except for T5, any connected 5-chromatic oriented digraph in which each vertex has out-degree at least two contains a copy of P4. It will be shown, by an example, that the condition that each vertex has out-degree at least two is indispensable.

Soit T5 le tournoi régulier contenant cinq sommets. B. Grünbaum a prouvé que T5 est le seul 5-tournoi qui ne contient pas le chemin antidirigé P4. Nous prouvons dans cette Note que T5 est le seul graphe orienté 5-chromatique dans lequel tout sommet a un degré extérieur au moins deux qui ne contient pas le chemin antidirigé P4. On prouve à l'aide d'un exemple que la condition « tout sommet a un degré exterieur au moins deux » est indispensable.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.06.028

Amine El Sahili 1

1 Section I, Sciences Faculty, Lebanese University, Beyrouth, Lebanon
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Amine El Sahili. Antidirected paths in 5-chromatic digraphs. Comptes Rendus. Mathématique, Volume 339 (2004) no. 5, pp. 317-320. doi : 10.1016/j.crma.2004.06.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.028/

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