Tournaments and colouring

Eli Berger, Krzysztof Choromanski, Maria Chudnovsky, Jacob Fox, Martin Loebl, Alex Scott, Paul Seymour, Stéphan Thomassé

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalJournal of Combinatorial Theory. Series B
Issue number1
StatePublished - Jan 2013

Bibliographical note

Funding 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.


  • Colouring
  • Erdos-Hajnal conjecture
  • Tournament
  • Transitive

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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