✦ LIBER ✦
Piercing convex sets and the Hadwiger-Debrunner (p, q)-problem
✍ Scribed by Noga Alon; Daniel J Kleitman
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 573 KB
- Volume
- 96
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
✦ Synopsis
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) < cc such that for every family % 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 9. This settles an old problem of Hadwiger and Debrunner.