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arXiv · 0906.2924

Lower Bounds for Pinning Lines by Balls

Otfried Cheong·Xavier Goaoc·Andreas Holmsen
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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.

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Otfried Cheong, Xavier Goaoc, Andreas Holmsen. 2009-06-16. Lower Bounds for Pinning Lines by Balls. https://arxiv.org/abs/0906.2924

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