Computing the clique number of tournaments
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866910298346094592 |
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| author | Aubian, Guillaume |
| author_facet | Aubian, Guillaume |
| contents | The clique number of a tournament is the maximum clique number of a graph formed by keeping backwards arcs in an ordering of its vertices. We study the time complexity of computing the clique number of a tournament and prove that, for any integer $k \geq 3$, deciding whether a tournament has clique number at most $k$ is NP-complete. This answers an interrogation of Nguyen, Scott and Seymour. To do so, we make use of a construction which we then modify to provide a counterexample to a conjecture of Aboulker, Aubian, Charbit and Lopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07776 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing the clique number of tournaments Aubian, Guillaume Combinatorics Discrete Mathematics The clique number of a tournament is the maximum clique number of a graph formed by keeping backwards arcs in an ordering of its vertices. We study the time complexity of computing the clique number of a tournament and prove that, for any integer $k \geq 3$, deciding whether a tournament has clique number at most $k$ is NP-complete. This answers an interrogation of Nguyen, Scott and Seymour. To do so, we make use of a construction which we then modify to provide a counterexample to a conjecture of Aboulker, Aubian, Charbit and Lopes. |
| title | Computing the clique number of tournaments |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2401.07776 |