Piercing convex sets and the Hadwiger-Debrunner (p, q)-problem

Noga Alon*, Daniel J. Kleitman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 J 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 J. This settles an old problem of Hadwiger and Debrunner.

Original languageEnglish
Pages (from-to)103-112
Number of pages10
JournalAdvances in Mathematics
Volume96
Issue number1
DOIs
StatePublished - Nov 1992

Funding

FundersFunder number
U.S. Air Force

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