A new perspective from hypertournaments to tournaments
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917573148278784 |
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| author | Ai, Jiangdong Dai, Qiming Guo, Qiwen Hu, Yingqi Wang, Changxin |
| author_facet | Ai, Jiangdong Dai, Qiming Guo, Qiwen Hu, Yingqi Wang, Changxin |
| contents | A $k$-tournament $H$ on $n$ vertices is a pair $(V, A)$ for $2\leq k\leq n$, where $V(H)$ is a set of vertices, and $A(H)$ is a set of all possible $k$-tuples of vertices, such that for any $k$-subset $S$ of $V$, $A(H)$ contains exactly one of the $k!$ possible permutations of $S$. In this paper, we investigate the relationship between a hyperdigraph and its corresponding normal digraph. Particularly, drawing on a result from Gutin and Yeo, we establish an intrinsic relationship between a strong $k$-tournament and a strong tournament, which enables us to provide an alternative (more straightforward and concise) proof for some previously known results and get some new results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new perspective from hypertournaments to tournaments Ai, Jiangdong Dai, Qiming Guo, Qiwen Hu, Yingqi Wang, Changxin Combinatorics A $k$-tournament $H$ on $n$ vertices is a pair $(V, A)$ for $2\leq k\leq n$, where $V(H)$ is a set of vertices, and $A(H)$ is a set of all possible $k$-tuples of vertices, such that for any $k$-subset $S$ of $V$, $A(H)$ contains exactly one of the $k!$ possible permutations of $S$. In this paper, we investigate the relationship between a hyperdigraph and its corresponding normal digraph. Particularly, drawing on a result from Gutin and Yeo, we establish an intrinsic relationship between a strong $k$-tournament and a strong tournament, which enables us to provide an alternative (more straightforward and concise) proof for some previously known results and get some new results. |
| title | A new perspective from hypertournaments to tournaments |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.13563 |