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

Mathematics

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

42 Scopus citations

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 (US)
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

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Keywords

Colouring
Erdos-Hajnal conjecture
Tournament
Transitive

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10.1016/j.jctb.2012.08.003

Cite this

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title = "Tournaments and colouring",

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.",

keywords = "Colouring, Erdos-Hajnal conjecture, Tournament, Transitive",

author = "Eli Berger and Krzysztof Choromanski and Maria Chudnovsky and Jacob Fox and Martin Loebl and Alex Scott and Paul Seymour and St{\'e}phan Thomass{\'e}",

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.",

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AU - Berger, Eli

AU - Choromanski, Krzysztof

AU - Chudnovsky, Maria

AU - Fox, Jacob

AU - Loebl, Martin

AU - Scott, Alex

AU - Seymour, Paul

AU - Thomassé, Stéphan

N1 - 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.

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KW - Colouring

KW - Erdos-Hajnal conjecture

KW - Tournament

KW - Transitive

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Tournaments and colouring

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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