## Otfried Cheong, Helly-Type Theorems for Line-Transversals to Spheres

Helly-Type Theorems for Line-Transversals to Spheres
Otfried Cheong
Div. of Computer Science, KAIST, Daejeon, Korea.
2008/03/06 Thu, 3PM-4PM

We prove Helly-type theorems for line transversals to disjoint unit spheres in Rd. In particular, we show that a family of n ≥ 2d disjoint unit spheres in Rd has a line transversal if, for some ordering of the balls, any subfamily of 2d balls admits a line transversal consistent with this ordering. We also discuss generalizations that drop the ordering requirement and to spheres with arbitrary radius.

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