Some results and problems on tournament structure
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916409132449792 |
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| author | Nguyen, Tung Scott, Alex Seymour, Paul |
| author_facet | Nguyen, Tung Scott, Alex Seymour, Paul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02364 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some results and problems on tournament structure Nguyen, Tung Scott, Alex Seymour, Paul Combinatorics 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. |
| title | Some results and problems on tournament structure |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2306.02364 |