A Helly-type theorem for line transversals to disjoint unit balls

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Let F be a family of disjoint unit balls in R-3. We prove that there is a Hellynumber no less than or equal to 46, such that if every n(o) members of F (\F\ greater than or equal to n(0)) have a line transversal, then T has a line transversal. In order to prove this we prove that if the members of F can be ordered in a way such that every 12 members of F are met by a line consistent with the ordering, then F has a line transversal. The proof also uses the recent result on geometric permutations for disjoint unit balls by Katchalski, Suri, and Zhou.
Publisher
Springer
Issue Date
2003-06
Language
English
Article Type
Article
Citation

DISCRETE COMPUTATIONAL GEOMETRY, v.29, no.4, pp.595 - 602

ISSN
0179-5376
DOI
10.1007/s00454-002-0793-0
URI
http://hdl.handle.net/10203/78481
Appears in Collection
MA-Journal Papers(저널논문)
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