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 P 3-convexity on graphs. P 3-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.
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Dourado, M.C., Rautenbach, D., dos Santos, V.F., Schäfer, P.M., Szwarcfiter, J.L., Toman, A. (2012). On the Radon Number for P 3-Convexity. In: Fernández-Baca, D. (eds) LATIN 2012: Theoretical Informatics. LATIN 2012. Lecture Notes in Computer Science, vol 7256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29344-3_23
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DOI: https://doi.org/10.1007/978-3-642-29344-3_23
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