Score lists in (h,k)-bipartite hypertournaments

Abstract

Given non-negative integers m, n, h and k with m ≥ h > 1 and n ≥ 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| = n, and |V| = n, and A is a set of (h + k)-tuples of vertices, called arcs, with at most h vertices from U and at most k vertices from V, such that for any h + k subsets U 1 ∪ V 1 of U ∪ V, A contains exactly one of the (h + k)! (h + k)-tuples whose entries belong to U 1 ∪ V 1. 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 are obtained.