On the radon number for p3 convexity

Authors:
Mitre C. Dourado;Dieter Rautenbach;Vinícius Fernandes dos Santos;Philipp M. Schäfer;Jayme L. Szwarcfiter;Alexandre Toman
Affiliations:
Instituto de Matematica, 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;Institut für Optimierung und Operations Research, Universität Ulm, Ulm, Germany;Instituto de Matematica, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil and PESC, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil and NCE, Universidade Federa ...;Instituto de Matematica, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
Venue:
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Year:
2012

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Abstract

The generalization of classical results about convex sets in ℝn to abstract convexity spaces, defined by sets of paths in graphs, leads to many challenging structural and algorithmic problems. Here we study the Radon number for the P3-convexity on graphs. P3-convexity has been proposed in connection with rumour and disease spreading processes in networks and the Radon number allows generalizations of Radon's classical convexity result. We establish hardness results, describe efficient algorithms for trees, and prove a best-possible bound on the Radon number of connected graphs.