Helly-type theorems for line transversals to disjoint unit balls

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We prove Helly-type theorems for line transversals to disjoint unit balls in R-d. In particular, we show that a family of n >= 2d disjoint unit balls in R-d has a line transversal if, for some ordering < of the balls, any subfamily of 2d balls admits a line transversal consistent with <. We also prove that a family of n >= 4d-1 disjoint unit balls in R-d admits a line transversal if any subfamily of size 4d-1 admits a transversal.
Publisher
SPRINGER
Issue Date
2008-03
Language
ENG
Article Type
Article; Proceedings Paper
Keywords

GEOMETRIC PERMUTATIONS; COMMON TRANSVERSALS; CONJECTURE; GRUNBAUM; SPHERES

Citation

DISCRETE & COMPUTATIONAL GEOMETRY, v.39, pp.194 - 212

ISSN
0179-5376
URI
http://hdl.handle.net/10203/7725
Appears in Collection
CS-Journal Papers(저널논문)MA-Journal Papers(저널논문)
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