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Some results and problems on tournament structure

Abstract:
This paper is a survey of results and problems related to the following question: is it true that if G is a tournament with sufficiently large chromatic number, then G has two vertex-disjoint subtournaments A, B, both with large chromatic number, such that all edges between them are directed from A to B? We describe what we know about this question, and report some progress on several other related questions, on tournament colouring and domination.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.jctb.2025.02.002

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Merton College
Role:
Author
ORCID:
0000-0003-4489-5988


More from this funder
Funder identifier:
https://ror.org/0439y7842
Grant:
EP/X013642/1


Publisher:
Elsevier
Journal:
Journal of Combinatorial Theory, Series B More from this journal
Volume:
173
Pages:
146-183
Publication date:
2025-02-28
Acceptance date:
2025-01-23
DOI:
EISSN:
1096-0902
ISSN:
0095-8956


Language:
English
Keywords:
Pubs id:
2083031
Local pid:
pubs:2083031
Deposit date:
2025-02-03

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