On two-path convexity in multipartite tournaments

Authors:
Darren B. Parker;Randy F. Westhoff;Marty J. Wolf
Affiliations:
Department of Mathematics, University of Dayton, Dayton, OH 45469, USA;Department of Mathematics and Computer Science, Bemidji State University, Bemidji, MN 56601, USA;Department of Mathematics and Computer Science, Bemidji State University, Bemidji, MN 56601, USA
Venue:
European Journal of Combinatorics
Year:
2008

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Abstract

In the context of two-path convexity, we study the rank, Helly number, Radon number, Caratheodory number, and hull number for multipartite tournaments. We show the maximum Caratheodory number of a multipartite tournament is 3. We then derive tight upper bounds for rank in both general multipartite tournaments and clone-free multipartite tournaments. We show that these same tight upper bounds hold for the Helly number, Radon number, and hull number. We classify all clone-free multipartite tournaments of maximum Helly number, Radon number, hull number, and rank.