Piercing convex sets

Noga Alon, Daniel J. Kleitman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A family of sets has the (p,q) property if among any p members of the family some q have a nonempty intersection. It is shown that for every p ≥ q ≥ d+1 there is a c = c(p,q,d) < ∞ such that for every family F of compact, convex sets in Rd which has the (p,q) property there is a set of at most c points in Rd that intersects each member of F. This extends Helly's Theorem and settles an old problem of Hadwiger and Debrunner.

Original languageEnglish
Title of host publicationEighth Annual Symposium On Computational Geometry
PublisherAssociation for Computing Machinery (ACM)
Pages157-160
Number of pages4
ISBN (Print)0897915178, 9780897915175
DOIs
StatePublished - 1992
EventEighth Annual Symposium On Computational Geometry - Berlin, Ger
Duration: 10 Jun 199212 Jun 1992

Publication series

NameEighth Annual Symposium On Computational Geometry

Conference

ConferenceEighth Annual Symposium On Computational Geometry
CityBerlin, Ger
Period10/06/9212/06/92

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