Score lists in multipartite hypertournaments

Abstract

Given non-negative integers $n_i$ and ${\alpha }_i$ with $0\le {\alpha }_i\le n_i$ $(i=1,2,...,k)$, an $[{\alpha }_1,{\alpha }_2,...,{\alpha }_k]$-$k$-partite hypertournament on ${\sum }_1^k{n}_i$ vertices is a $(k+1)$-tuple $(U_1,U_2,...,U_k,E)$, where $U_i$ are $k$ vertex sets with $|U_i|=n_i$, and $E$ is a set of ${\sum }_1^k{\alpha }_i$-tuples of vertices, called arcs, with exactly ${\alpha }_i$ vertices from $U_i$, such that any ${\sum }_1^k{\alpha }_i$ subset ${\cup }_1^k{U}_i^{\prime }$ of ${\cup }_1^k{U}_i$, $E$ contains exactly one of the $({\sum }_1^k{\alpha }_i)!$ ${\sum }_1^k{\alpha }_i$-tuples whose entries belong to ${\cup }_1^k{U}_i^{\prime }$. We obtain necessary and sufficient conditions for $k$ lists of non-negative integers in non-decreasing order to be the losing score lists and to be the score lists of some $k$-partite hypertournament.

References in corpus (1)

• On k-hypertournament losing scores