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Helly‐type theorems for the diameter

Helly‐type theorems for the diameter We study versions of Helly's theorem that guarantee that the intersection of a family of convex sets in Rd has a large diameter. This includes colourful, fractional and (p,q) versions of Helly's theorem. In particular, the fractional and (p,q) versions work with conditions where the corresponding Helly's theorem does not. We also include variants of Tverberg's theorem, Bárány's point selection theorem and the existence of weak epsilon‐nets for convex sets with diameter estimates. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Helly‐type theorems for the diameter

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References (41)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/bdw027
Publisher site
See Article on Publisher Site

Abstract

We study versions of Helly's theorem that guarantee that the intersection of a family of convex sets in Rd has a large diameter. This includes colourful, fractional and (p,q) versions of Helly's theorem. In particular, the fractional and (p,q) versions work with conditions where the corresponding Helly's theorem does not. We also include variants of Tverberg's theorem, Bárány's point selection theorem and the existence of weak epsilon‐nets for convex sets with diameter estimates.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Aug 1, 2016

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