SCORE LISTS IN (h, k)-BIPARTITE HYPERTOURNAMENTS

摘要

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| = m 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.