Hadwiger and Helly-type theorems for disjoint unit spheres in R3

Abstract : Let S be an ordered set of disjoint unit spheres in R3 We show that if every subset of at most six spheres from S admits a line transversal respecting the ordering, then the entire family has a line transversal. Without the order condition, we show that the existence of a line transversal for every subset of at most 11 spheres from S implies the existence of a line transversal forS.
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Otfried Cheong, Xavier Goaoc, Andreas Holmsen. Hadwiger and Helly-type theorems for disjoint unit spheres in R3. 21st Annual ACM Symposium on Computational Geometry 2005 (SoCG'05 ), Jun 2005, Pisa, Italy. pp.10-15, ⟨10.1145/1064092.1064097⟩. ⟨inria-00000206⟩

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