PIERCING CONVEX-SETS AND THE HADWIGER-DEBRUNNER (P, Q)-PROBLEM

被引：103

作者：

ALON, N

KLEITMAN, DJ

机构：

[1] BELL COMMUN RES INC,MORRISTOWN,NJ 07960

[2] MIT,DEPT MATH,CAMBRIDGE,MA 02139

来源：

ADVANCES IN MATHEMATICS | 1992年 / 96卷 / 01期

关键词：

D O I：

10.1016/0001-8708(92)90052-M

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. © 1992.

引用

页码：103 / 112

页数：10