Geometric permutations of disjoint unit spheres

Citations of this article
Mendeley users who have this article in their library.
Get full text


We show that a set of n disjoint unit spheres in Rd admits at most two distinct geometric permutations if n≥9, and at most three if 3≤n≤8. This result improves a Helly-type theorem on line transversals for disjoint unit spheres in R3: if any subset of size at most 18 of a family of such spheres admits a line transversal, then there is a line transversal for the entire family. © 2004 Elsevier B.V.




Cheong, O., Goaoc, X., & Na, H. S. (2005). Geometric permutations of disjoint unit spheres. Computational Geometry: Theory and Applications, 30(3), 253–270.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free