The Katchalski-Lewis transversal problem in R-n

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Let F be a family of disjoint translates of a compact convex set in the plane. In 1980 Katchalski and Lewis showed that there exists a constant k, independent of F, such that if each three members of F are met by a line, then a "large" subfamily G subset of F, with |F\G| <= k, is met by a line. In this paper we obtain a higher-dimensional analogue containing the Katchalski-Lewis result. Also we give two constructions of families of pairwise disjoint translates of the unit ball in R-3 which answer some related questions.
Publisher
SPRINGER
Issue Date
2007-03
Language
English
Article Type
Article
Keywords

HYPERPLANE TRANSVERSALS; LINE TRANSVERSALS; UNIT BALLS

Citation

DISCRETE COMPUTATIONAL GEOMETRY, v.37, no.3, pp.341 - 349

ISSN
0179-5376
DOI
10.1007/s00454-006-1291-6
URI
http://hdl.handle.net/10203/90604
Appears in Collection
MA-Journal Papers(저널논문)
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