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Lower Bounds to Helly Numbers of Line Transversals to Disjoint Congruent 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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https://hal.inria.fr/inria-00518035
Contributor : Xavier Goaoc Connect in order to contact the contributor
Submitted on : Thursday, September 16, 2010 - 12:21:32 PM
Last modification on : Tuesday, June 28, 2022 - 10:04:35 AM

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  • HAL Id : inria-00518035, version 1

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Otfried Cheong, Xavier Goaoc, Andreas Holmsen. Lower Bounds to Helly Numbers of Line Transversals to Disjoint Congruent Balls. Israel Journal of Mathematics, 2012, 190 (1), pp.213-228. ⟨inria-00518035⟩

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