Piercing convex sets

Noga Alon, Daniel J. Kleitman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


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 (US)
Title of host publicationEighth Annual Symposium On Computational Geometry
PublisherPubl by ACM
Number of pages4
ISBN (Print)0897915178, 9780897915175
StatePublished - 1992
Externally publishedYes
EventEighth Annual Symposium On Computational Geometry - Berlin, Ger
Duration: Jun 10 1992Jun 12 1992

Publication series

NameEighth Annual Symposium On Computational Geometry


OtherEighth Annual Symposium On Computational Geometry
CityBerlin, Ger

All Science Journal Classification (ASJC) codes

  • General Engineering


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