On scores in multipartite hypertournaments

Abstract

In this paper, we discuss two types of hypertournaments, one [α_i]₁^k-multipartite hypertournament ([α_i]₁^k-MHT) and the second (α_i)_k-multipartite hypertournament ((α_i)_k-MHT). We obtain necessary and sufficient conditions for the k lists of non-negative integers in non-decreasing order to be the losing score lists (score lists) of [α_i]₁^k-MHT and that of (α_i)_k-MHT. We extend this concept to more general class of [α_i]₁^k-multipartite multihypertournament ([α_i]₁^k-MMHT) and (α_i)_k-multipartite multihypertournament ((α_i)_k-MMHT).