Geometric permutations of disjoint unit spheres

DOI10.1016/j.comgeo.2004.08.003zbMath1076.52002OpenAlexW2155081398MaRDI QIDQ1776899

Hyeon-Suk Na, Xavier Goaoc, Otfried Schwarzkopf

Publication date: 12 May 2005

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.comgeo.2004.08.003

zbMATH Keywords

geometric transversalsHelly-type results

Mathematics Subject Classification ID

Helly-type theorems and geometric transversal theory (52A35) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (8)

Geometric permutations of non-overlapping unit balls revisited ⋮ INFLATING BALLS IS NP-HARD ⋮ Helly numbers of acyclic families ⋮ Line transversals to disjoint balls ⋮ Helly-type theorems for line transversals to disjoint unit balls ⋮ Some Discrete Properties of the Space of Line Transversals to Disjoint Balls ⋮ Unnamed Item ⋮ The \(T(4)\) property of families of unit disks

Cites Work

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• Upper bounds on geometric permutations for convex sets
• The maximum number of ways to stab n convex nonintersecting sets in the plane is 2n-2
• Geometric permutations of disjoint translates of convex sets
• The different ways of stabbing disjoint convex sets
• A constant bound for geometric permutations of disjoint unit balls
• A Helly-type theorem for line transversals to disjoint unit balls
• Sharp bounds on geometric permutations of pairwise disjoint balls in \(\mathbb{R}^d\)
• Forbidden families of geometric permutations in \(\mathbb R^{d}\)
• Algorithms - ESA 2003
• The triples of geometric permutations for families of disjoint translates
• A tight bound on the number of geometric permutations of convex fat objects in \(\mathbb{R}^d\)

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