Advertisement
Published in:
2012 | OriginalPaper | Chapter
On the Radon Number for P 3-Convexity
Authors : Mitre C. Dourado, Dieter Rautenbach, Vinícius Fernandes dos Santos, Philipp M. Schäfer, Jayme L. Szwarcfiter, Alexandre Toman
Published in: LATIN 2012: Theoretical Informatics
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
The generalization of classical results about convex sets in ℝ
n
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.