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Helly-Type Theorems for Line Transversals to Disjoint Unit Balls

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.
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Contributor : Xavier Goaoc Connect in order to contact the contributor
Submitted on : Tuesday, February 6, 2007 - 4:06:31 PM
Last modification on : Wednesday, February 2, 2022 - 3:51:34 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 6:27:47 PM


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



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