Helly-Type Theorems for Line Transversals to Disjoint Unit Balls

We prove Helly-type theorems for line transversals to disjoint unit balls in Rd . 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, any subfamily of 2d balls admits a line transversal consistent with . We also prove that a family of n 4d - 1 disjoint unit balls in Rd admits a line transversal if any subfamily of size 4d - 1 admits a transversal.

• Type: Journal
• Year: 2008
• Where: DCG
• Authors: Otfried Cheong, Xavier Goaoc, Andreas Holmsen, Sylvain Petitjean
• Keywords: DCG 2008, Line Transversals, Transversal, Unit Balls