Characterization and recognition of Radon-independent sets in split graphs

Authors:
Mitre C. Dourado;Dieter Rautenbach;ViníCius Fernandes Dos Santos;Jayme L. Szwarcfiter
Affiliations:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;Institut für Optimierung und Operations Research, Universität Ulm, Ulm, Germany;PESC, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil and PESC, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
Venue:
Information Processing Letters
Year:
2012

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Abstract

Let R be a set of vertices of a split graph G. We characterize when R allows a partition into two disjoint set R"1 and R"2 such that the convex hulls of R"1 and R"2 with respect to the P"3-convexity of G intersect. Furthermore, we describe a linear time algorithm that decides the existence of such a partition. Our results are related to the so-called Radon number of the P"3-convexity of G and complement earlier results in this area.