The covering radius problem for sets of 1-factors of the complete uniform hypergraphs

Abstract

a b s t r a c tCovering and packing problems constitute a class of questions concerning finite metric spaces that have surfaced in recent literature. In this paper, we consider, for the first time, these problems for the finite metric space (Ω, d) arising from the set Ω of 1-factors of the complete t-uniform hypergraph H on nt vertices for some positive integers n and t. We focus on the covering problem; in particular we investigate bounds on the covering radius of any code C ⊆ Ω. In doing so, we give both upper and lower bounds on the covering radius, as well as a frequency parameter type result that follows from the Lovász local lemma.