Score lists in [h-k]-bipartite hypertournaments

Abstract

Given non-negative integers m, n, h and k with $ m\geq h>1 $ and $ n\geq k>1, $an [h-k]-bipartite hypertournament on $ m+n$ vertices is a triple $(U,V,A) $, where U and V are two sets of vertices with $| U| =m$ and $ | V| =n,$ and $A$ is a set of $(h+k) -$ tuples of vertices, called arcs, with exactly $h$ vertices from $U$ and exactly $k$ vertices from $V$, such that any $h+k$ subsets $ U_{1}\cup V_{1}$ of $U\cup V, A$ contains exactly one of the $(h+k) ! (h+k) -$tuples whose entries belong to $U_{1}\cup V_{1}.$ We obtain necessary and sufficient conditions for a pair of non-decreasing sequences of non-negative integers to be the losing score lists or score lists of some$[h-k]-$bipartite hypertournament.\bigskip