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arXiv · 2401.13563

A new perspective from hypertournaments to tournaments

Jiangdong Ai·Qiming Dai·Qiwen Guo·Yingqi Hu·Changxin Wang
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Abstract

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.

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Jiangdong Ai, Qiming Dai, Qiwen Guo, Yingqi Hu, Changxin Wang. 2024-01-24. A new perspective from hypertournaments to tournaments. https://arxiv.org/abs/2401.13563

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