On the Spectrum of Minimal Covers By Triples

Abstract

A Minimal Cover by Triples is an ordered pair (V,T) where V is a finite set and T is a collection of three element subsets of V with two properties. First, that every pair of elements of V appear together in at least one element of T. Second, if any element of T is removed the first property no longer holds. In this dissertation we explore the possible values |T| can take on for a given |V|. In addition, construction techniques are given to construct a Minimal Cover by Triples for given values of |V| and |T|.