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

摘要

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 forS.