Hadwiger and Helly-type theorems for disjoint unit spheres in R3

Let S be an ordered set of disjoint unit spheres in R3 . We show that if every subset of at most six spheres from S admits a line transversal respecting the ordering, then the entire family has a line transversal. Without the order condition, we show that the existence of a line transversal for every subset of at most 11 spheres from S implies the existence of a line transversal for S. Categories and Subject Descriptors: F.2.2 [Nonnumerical Algorithms and Problems]: Geometrical problems and computations General Terms: Theory

• Type: Conference
• Year: 2005
• Where: COMPGEOM
• Authors: Otfried Cheong, Xavier Goaoc, Andreas Holmsen
• Keywords: COMPGEOM 2005, Discrete Geometry, Disjoint Unit, Line Transversal, Spheres