A Direct Construction of Transversal Covers Using Group Divisible Designs

Abstract

A transversal cover is a set of $gk$ points in $k$ disjoint groups of size $g$ and, ideally, a minimal collection of transversal subsets, called blocks, such that any pair of points not contained in the same group appears in at least one block. In this article we present a direct construction method for transversal covers using group divisible designs. We also investigate a particular infinite family of group divisible designs that yield particularly good covers.