The (2,2) and (4,3) Properties in Families of Fat Sets in the Plane

DOI10.1137/17M1157088zbMath1422.52003arXiv1711.05308MaRDI QIDQ5232156

Shiliang Gao, Shira Zerbib

Publication date: 29 August 2019

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.05308

zbMATH Keywords

convex setspiercing numbersfat sets\((2, 2)\) property\((4, 3)\) property\((p, q)\) property

Mathematics Subject Classification ID

Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Convex sets in (2) dimensions (including convex curves) (52A10) Helly-type theorems and geometric transversal theory (52A35) Combinatorial complexity of geometric structures (52C45)

Related Items (1)

Bounds on piercing and line-piercing numbers in families of convex sets in the plane

Cites Work

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• Über eine Variante zum Hellyschen Satz
• Piercing families of convex sets with the \(d\)-intersection property in \(\mathbb R^{d}\)
• The maximum piercing number for some classes of convex sets with the \((4,3)\)-property
• Piercing convex sets and the Hadwiger-Debrunner \((p,q)\)-problem
• On Max-Clique for intersection graphs of sets and the Hadwiger-Debrunner numbers
• Convex sets in the plane with three of every four meeting

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