Tournaments and colouring

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

doi:10.1016/j.jctb.2012.08.003

Tournaments and colouring

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Journal of Combinatorial Theory. Series B
Volume	103
Issue number	1
DOIs	https://doi.org/10.1016/j.jctb.2012.08.003
State	Published - 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.

Keywords

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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10.1016/j.jctb.2012.08.003

Cite this

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AU - Scott, Alex

AU - Seymour, Paul

AU - Thomassé, Stéphan

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Tournaments and colouring

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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