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.
Bibliographical noteFunding Information:
1 Supported by BSF grant 2006099. 2 Supported by NSF grant IIS-1117631. 3 Supported by NSF grants DMS-0758364 and DMS-1001091, and BSF grant 2006099. 4 Supported by a Simons Fellowship. 5 Supported by ONR grant N00014-10-1-0680 and NSF grant DMS-0901075.
- Erdos-Hajnal conjecture
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics