Score sequences in oriented k-hypergraphs

Abstract

Given two non-negative integers n and k with $n geq k >$ 1, an oriented k-hypergraph on n vertices is a pair (V,A), where V is a set of vertices with |V| = n and A is a set of k-tuples of vertices, called arcs, such that for any k-subset S of V, A contains at most one of the k! k-tuples whose entries belong to S. In this paper, we define the score of a vertex in an oriented k-hypergraph and then obtain a necessary and sufficient condition for the sequence of non-negative integers $[s_{1,} s_{2} , ^{...} , s_n ]$ to be a score sequence of some oriented k-hypergraph.