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Tournaments and colouring. (English) Zbl 1254.05064
Summary: A tournament is a complete graph with its edges directed, and colouring a tournament means partitioning its vertex set into transitive subtournaments. For some tournaments $$H$$ there exists $$c$$ such that every tournament not containing $$H$$ as a subtournament has chromatic number at most $$c$$ (we call such a tournament $$H$$ a hero); for instance, all tournaments with at most four vertices are heroes. In this paper we explicitly describe all heroes.

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C55 Generalized Ramsey theory 05C15 Coloring of graphs and hypergraphs
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