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Journal Articles Computational Geometry Year : 2005

Geometric Permutations of Disjoint Unit Spheres


We show that a set of $n$ disjoint unit spheres in $R^d$ admits at most two distinct geometric permutations if $n \geq 9$, and at most three if $3 \leq n \leq 8$. This result improves a Helly-type theorem on line transversals for disjoint unit spheres in $R^3$: if any subset of size $18$ of a family of such spheres admits a line transversal, then there is a line transversal for the entire family.
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inria-00000637 , version 1 (05-10-2006)


  • HAL Id : inria-00000637 , version 1


Otfried Cheong, Xavier Goaoc, Na Hyeon-Suk. Geometric Permutations of Disjoint Unit Spheres. Computational Geometry, 2005, 30 (3), pp.253-270. ⟨inria-00000637⟩
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