Lower Bounds for Pinning Lines by Balls
Computational Geometry
2009-06-17 v1
Abstract
A line L is a transversal to a family F of convex objects in R^d if it intersects every member of F. In this paper we show that for every integer d>2 there exists a family of 2d-1 pairwise disjoint unit balls in R^d with the property that every subfamily of size 2d-2 admits a transversal, yet any line misses at least one member of the family. This answers a question of Danzer from 1957.
Cite
@article{arxiv.0906.2924,
title = {Lower Bounds for Pinning Lines by Balls},
author = {Otfried Cheong and Xavier Goaoc and Andreas Holmsen},
journal= {arXiv preprint arXiv:0906.2924},
year = {2009}
}