Helly-type Theorems for Line transversals to Disjoint Unit Balls (Extended abstract)

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 >= 2d disjoint unit balls in Rd has a line transversal if, for some ordering of the balls, every subfamily of 2d balls admits a line transversal consistent with . We also prove that a family of n >= 4d − 1 disjoint unit balls in R^d admits a line transversal if every subfamily of size 4d − 1 admits a transversal.
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https://hal.inria.fr/inria-00189019
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Otfried Cheong, Xavier Goaoc, Andreas Holmsen, Sylvain Petitjean. Helly-type Theorems for Line transversals to Disjoint Unit Balls (Extended abstract). European Workshop on Computational Geometry, Mar 2006, Delphi, Greece. pp.87--89. ⟨inria-00189019⟩

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