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

Title:
Hadwiger and Helly-type theorems for disjoint unit spheres in R3
Authors:
Cheong, Otfried, Goaoc, Xavier, Holmsen, Andreas
Contributors:
Department of Electrical Engineering [Korea Advanced Institute of Science and Technology] (KAIST), Korea Advanced Institute of Science and Technology (KAIST), Effective Geometric Algorithms for Surfaces and Visibility (VEGAS), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Bergen] (UiB), University of Bergen (UiB)
Source:
21st Annual ACM Symposium on Computational Geometry 2005 (SoCG'05 ). :10-15
Publisher Information:
CCSD; ACM Press, 2005.
Publication Year:
2005
Collection:
collection:CNRS
collection:INRIA
collection:INPL
collection:INRIA-LORRAINE
collection:LORIA2
collection:INRIA-NANCY-GRAND-EST
collection:TESTALAIN1
collection:UNIV-LORRAINE
collection:INRIA2
collection:LORIA
collection:AM2I-UL
Subject Terms:
unit sphere, unit ball, line transversal, Helly theorem, Hadwiger theorem, ACM: F.: Theory of Computation, F.2: ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, F.2.2: Nonnumerical Algorithms and Problems, [INFO.INFO-DL]Computer Science [cs], Digital Libraries [cs.DL]
Subject Geographic:
Pisa, Italy
Original Identifier:
HAL:
Document Type:
Conference conferenceObject<br />Conference papers
Language:
English
Relation:
info:eu-repo/semantics/altIdentifier/doi/10.1145/1064092.1064097
DOI:
10.1145/1064092.1064097
Access URL:
https://inria.hal.science/inria-00000206
https://inria.hal.science/inria-00000206v1/document
https://inria.hal.science/inria-00000206v1/file/Helly-type-transversals-socg05.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.inria.00000206v1
Database:
HAL

Further Information

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.