Convexity and HHD-free graphs

Abstract

It is well-known that chordal graphs can be characterized via m-convexity. In this paper we introduce the notion of m"3-convexity (a relaxation of m-convexity) which is closely related to semisimplicial orderings of graphs. Using this notion we give simpler proofs of results from [8]and present some new characterizations of HHD-free graphs via m"3-convexity of disks. Moreover, we characterize weak bipolarizable graphs as the graphs for which the family of all m"3-convex sets is a convex geometry. As an application of our results we present a simple efficient criterion for deciding whether a HHD-free graph with given vertex radius function r is r-dominated by a clique. (orig.)Available from TIB Hannover: RR 1945(290) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman