A note on homomorphisms of Kneser hypergraphs

Abstract

Let n, k, r be positive integers, with n ≥ kr. The r-uniform Kneser hypergraph KGr(n, k) has as vertex set the set of all k-subsets of the set {1,…,n} and its (hyper) edges are formed by the r-tuples of pairwise disjoint k-subsets of the set {1,…,n}. In this paper, we give conditions for the existence of homomorphisms between uniform Kneser hypergraphs.