Lower Bounds for Pinning Lines by Balls
Abstract
A line L is a transversal to a family F of convex objects in Rd 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 Rd 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.
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