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Communication Dans Un Congrès Année : 2012

A Theorem of Barany Revisited and Extended

Résumé

The colorful Caratheodory theorem states that given d+1 sets of points in R^d, the convex hull of each containing the origin, there exists a simplex (called a 'rainbow simplex') with at most one point from each point set, which also contains the origin. Equivalently, either there is a hyperplane separating one of these d+1 sets of points from the origin, or there exists a rainbow simplex containing the origin. One of our results is the following extension of the colorful Caratheodory theorem: given d/2+1 sets of points in $R^d, and a convex object C, then either one set can be separated from C by a constant (depending only on d) number of hyperplanes, or there is a (d/2+1)-dimensional rainbow simplex intersecting C.
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Dates et versions

hal-00761355 , version 1 (05-12-2012)

Identifiants

  • HAL Id : hal-00761355 , version 1

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Nabil Mustafa, Ray Saurabh. A Theorem of Barany Revisited and Extended. 2012 Symposium on Computational Geometry, Jun 2012, United States. pp.333--338. ⟨hal-00761355⟩
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