Helly-type theorems for the diameter

DOI10.1112/blms/bdw027zbMath1353.52005arXiv1509.07908OpenAlexW2963886109MaRDI QIDQ3188360

Pablo Soberón

Publication date: 19 August 2016

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.07908

zbMATH Keywords

diameterHelly's theorem\((p, q)\) theorem\(v\)-width

Mathematics Subject Classification ID

Length, area, volume and convex sets (aspects of convex geometry) (52A38) Approximation by convex sets (52A27) Helly-type theorems and geometric transversal theory (52A35)

Related Items (7)

A Quantitative Helly-Type Theorem: Containment in a Homothet ⋮ Unnamed Item ⋮ Helly’s theorem: New variations and applications ⋮ Nerves, minors, and piercing numbers ⋮ Tverberg’s theorem is 50 years old: A survey ⋮ Quantitative combinatorial geometry for concave functions ⋮ A Mélange of Diameter Helly-Type Theorems

Cites Work

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• A simpler proof of the Boros-Füredi-Bárány-Pach-Gromov theorem
• Quantitative Helly-type theorem for the diameter of convex sets
• Singularities, expanders and topology of maps. II: From combinatorics to topology via algebraic isoperimetry
• Über eine Variante zum Hellyschen Satz
• Contraction and expansion of convex sets
• A generalization of Caratheodory's theorem
• Piercing convex sets and the Hadwiger-Debrunner \((p,q)\)-problem
• A Tverberg-type result on multicolored simplices
• Helly numbers of algebraic subsets of \(\mathbb{R}^{d}\) and an extension of Doignon's theorem
• Transversal numbers for hypergraphs arising in geometry
• A fractional Helly theorem for convex lattice sets
• Bounded VC-dimension implies a fractional Helly theorem
• Bounding the piercing number
• Helly's Theorem with Volumes
• Convex bodies, economic cap coverings, random polytopes
• A Problem of Geometry in R n
• Point Selections and Weak ε-Nets for Convex Hulls
• A Generalization of Radon's Theorem
• Proof of a conjecture of Bárány, Katchalski and Pach

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