Tournaments and colouring
Eli Berger, Krzysztof Choromański, Maria Chudnovsky, Jacob Fox, Martin Loebl, Alex Scott, Paul D. Seymour, Stéphan Thomassé · 2011
A tournament is a complete graph with its edges directed, and colouring a tournament means par-titioning 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. 1