# Helly-Type Theorems for Line Transversals to Disjoint Unit Balls

2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We prove Helly-type theorems for line transversals to disjoint unit balls in $\R^{d}$. In particular, we show that a family of $n \geq 2d$ disjoint unit balls in $\R^d$ has a line transversal if, for some ordering $\prec$ of the balls, any subfamily of $2d$ balls admits a line transversal consistent with $\prec$. We also prove that a family of $n \geq 4d-1$ disjoint unit balls in $\R^d$ admits a line transversal if any subfamily of size $4d-1$ admits a transversal.
Document type :
Journal articles

Cited literature [18 references]

https://hal.inria.fr/inria-00103856
Contributor : Xavier Goaoc <>
Submitted on : Tuesday, February 6, 2007 - 4:06:31 PM
Last modification on : Monday, June 24, 2019 - 12:32:04 PM
Long-term archiving on : Tuesday, April 6, 2010 - 6:27:47 PM

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Helly-for-transversals.pdf
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### Citation

Otfried Cheong, Xavier Goaoc, Andreas Holmsen, Sylvain Petitjean. Helly-Type Theorems for Line Transversals to Disjoint Unit Balls. Discrete and Computational Geometry, Springer Verlag, 2008, 39 (1-3), pp.194-212. ⟨inria-00103856⟩

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