Helly-Type Theorems for Line-Transversals to Spheres

Otfried Cheong

Div. of Computer Science, KAIST, Daejeon, Korea.

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 R^{d}. In particular, we show that a family of n ≥ 2d disjoint unit spheres in R^{d} 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.

Tags: OtfriedCheong