Score lists in [h-k]-bipartite hypertournaments

Abstract

Let m, n, h and k be integers such that m ≥ h > 1 and n ≥ k > 1. An [h-k]-bipartite hypertournament on m + n vertices is a triple (U, V, E), with two vertex sets U and V, |U| = m, |V| = n, together with an arc set E, a set of (h + k)-tuples of vertices, with exactly h vertices from U and exactly k vertices from V, called arcs, such that for any h-subset U1 of U and k-subset V1 of V, E contains exactly one of the (h + k)! (h + k)-tuples whose h entries belong to U1 and k entries belong to V1. We obtain necessary and sufficient conditions for a pair of nondecreasing sequences of nonnegative integers to be the losing score lists or score lists of some [h-k]-bipartite hypertournament.