2024/01/24 by Ai, Jiangdong, Dai, Qiming, Guo, Qiwen +2
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2401.13563
A k-tournament H on n vertices is a pair (V, A) for 2≤ k≤ 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.