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 -