Geometric permutations of disjoint unit spheres

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We show that a set of n disjoint unit spheres in R(d) 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 R 3 : 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. (c) 2004 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2005-03
Language
ENG
Article Type
Article
Keywords

CONVEX-SETS; LINE TRANSVERSALS; FAMILIES; NUMBER; BOUNDS; BALLS

Citation

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, v.30, pp.253 - 270

ISSN
0925-7721
DOI
10.1016/j.comgeo.2004.08.003
URI
http://hdl.handle.net/10203/299
Appears in Collection
CS-Journal Papers(저널논문)
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