Antidirected paths in 5-chromatic digraphs
Amine El Sahili · Comptes Rendus Mathématique · 2004
Let T 5 be the regular 5-tournament. B. Grünbaum proved that T 5 is the only 5-tournament which contains no copy of the antidirected path P 4 . In this Note, we prove that, except for T 5 , any connected 5-chromatic oriented digraph in which each vertex has out-degree at least two contains a copy of P 4 . It will be shown, by an example, that the condition that each vertex has out-degree at least two is indispensable.