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Comptes Rendus Mathématique
Volume 339, n° 5
pages 317-320 (septembre 2004)
Doi : 10.1016/j.crma.2004.06.028
Received : 16 June 2004 ;  accepted : 22 June 2004
Antidirected paths in 5-chromatic digraphs
Chemins antidirigés dans les graphes 5-chromatiques.
 

Amine El Sahili
Section I, Sciences Faculty, Lebanese University, Beyrouth, Lebanon 

Abstract

Let   be the regular 5-tournament. B. Grünbaum proved that   is the only 5-tournament which contains no copy of the antidirected path  . In this Note, we prove that, except for  , any connected 5-chromatic oriented digraph in which each vertex has out-degree at least two contains a copy of  . It will be shown, by an example, that the condition that each vertex has out-degree at least two is indispensable. To cite this article: A. El Sahili, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

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Résumé

Soit   le tournoi régulier contenant cinq sommets. B. Grünbaum a prouvé que   est le seul 5-tournoi qui ne contient pas le chemin antidirigé  . Nous prouvons dans cette Note que   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  . On prouve à lʼaide dʼun exemple que la condition « tout sommet a un degré exterieur au moins deux » est indispensable. Pour citer cet article : A. El Sahili, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.


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