A Direct Construction of Transversal Covers Using Group Divisible Designs

Brett Stevens1, Alan Ling2, Eric Mendelsohn3
1Department of Mathematics and Statistics Simon Fraser University Burnaby BC V5L 186 Canada
2Department of Mathematical Sciences Michigan Technological University 1400 Townsend Drive Houghton, MI U.S.A. 49931-1295
3Department of Mathematics University of Toronto 100 St. George St. Toronto ON M6G 3G83 Canada

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.