Article

Hadwiger and Helly-type theorems for disjoint unit spheres in R³

Authors:

Otfried Cheong,

Andreas HolmsenAuthors Info & Claims

SCG '05: Proceedings of the twenty-first annual symposium on Computational geometry

Pages 10 - 15

https://doi.org/10.1145/1064092.1064097

Published: 06 June 2005 Publication History

Abstract

Let S be an ordered set of disjoint unit spheres in R³ We show that if every subset of at most six spheres from S admits a line transversal respecting the ordering, then the entire family has a line transversal. Without the order condition, we show that the existence of a line transversal for every subset of at most 11 spheres from S implies the existence of a line transversal forS.

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O. Cheong, X. Goaoc, and H.-S. Na. Geometric permutations of disjoint unit spheres. Comput. Geom. Theory Appl., 2005. In press.

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Cited By

Asinowski AKatchalski M(2019)The Maximal Number of Geometric Permutations for n Disjoint Translates of a Convex Set in ź Is Ω(n)Discrete & Computational Geometry10.1007/s00454-005-1219-635:3(473-480)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.1007/s00454-005-1219-6
Goaoc X(2009)Some Discrete Properties of the Space of Line Transversals to Disjoint BallsNonlinear Computational Geometry10.1007/978-1-4419-0999-2_3(51-83)Online publication date: 9-Oct-2009
https://doi.org/10.1007/978-1-4419-0999-2_3
Cheong OGoaoc XHolmsen APetitjean S(2008)Helly-Type Theorems for Line Transversals to Disjoint Unit BallsDiscrete & Computational Geometry10.5555/3116660.311699739:1-3(194-212)Online publication date: 1-Mar-2008
https://dl.acm.org/doi/10.5555/3116660.3116997

Index Terms

Hadwiger and Helly-type theorems for disjoint unit spheres in R³
1. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

SCG '05: Proceedings of the twenty-first annual symposium on Computational geometry

June 2005

398 pages

ISBN:1581139918

DOI:10.1145/1064092

Program Chairs:
Joe Mitchell
SUNY Stony Brook
,
Günter Rote
Freie Universität Berlin

Copyright © 2005 ACM.

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Published: 06 June 2005

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SoCG05: The 21st Annual ACM Symposium on Computational Geometry 2005

June 6 - 8, 2005

Pisa, Italy

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SCG '05 Paper Acceptance Rate 41 of 141 submissions, 29%;

Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Asinowski AKatchalski M(2019)The Maximal Number of Geometric Permutations for n Disjoint Translates of a Convex Set in ź Is Ω(n)Discrete & Computational Geometry10.1007/s00454-005-1219-635:3(473-480)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.1007/s00454-005-1219-6
Goaoc X(2009)Some Discrete Properties of the Space of Line Transversals to Disjoint BallsNonlinear Computational Geometry10.1007/978-1-4419-0999-2_3(51-83)Online publication date: 9-Oct-2009
https://doi.org/10.1007/978-1-4419-0999-2_3
Cheong OGoaoc XHolmsen APetitjean S(2008)Helly-Type Theorems for Line Transversals to Disjoint Unit BallsDiscrete & Computational Geometry10.5555/3116660.311699739:1-3(194-212)Online publication date: 1-Mar-2008
https://dl.acm.org/doi/10.5555/3116660.3116997

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