TY - JOUR

T1 - Piercing convex sets and the Hadwiger-Debrunner (p, q)-problem

AU - Alon, Noga

AU - Kleitman, Daniel J.

N1 - Funding Information:
* Research supported in part by Grant, and a U.S. Air Force Ofice

PY - 1992/11

Y1 - 1992/11

N2 - 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.

AB - 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.

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U2 - 10.1016/0001-8708(92)90052-M

DO - 10.1016/0001-8708(92)90052-M

M3 - Article

AN - SCOPUS:38249009255

SN - 0001-8708

VL - 96

SP - 103

EP - 112

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -