Lower Bounds for Pinning Lines by Balls

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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Submitted on : Tuesday, June 16, 2009 - 2:52:33 PM
Last modification on : Monday, June 24, 2019 - 12:32:04 PM
Long-term archiving on : Friday, June 11, 2010 - 12:51:06 AM

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  • HAL Id : inria-00395837, version 1
  • ARXIV : 0906.2924

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Otfried Cheong, Xavier Goaoc, Andreas Holmsen. Lower Bounds for Pinning Lines by Balls. [Research Report] RR-6961, INRIA. 2009, pp.12. ⟨inria-00395837⟩

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