Every large point set contains many collinear points or an empty pentagon

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/11669

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.contributor	Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.contributor.author	Wood, David
dc.contributor.author	Por, Attila
dc.contributor.author	Abel, Zachary
dc.contributor.author	Ballinger, Brad
dc.contributor.author	Bose, Prosenjit
dc.contributor.author	Collette, Sébastien
dc.contributor.author	Dujmovic, Vida
dc.contributor.author	Hurtado Díaz, Fernando Alfredo
dc.contributor.author	Kominers, Scott Duke
dc.contributor.author	Langerman, Stefan
dc.date	2011-01
dc.identifier.citation	Abel, Z. [et al.]. Every large point set contains many collinear points or an empty pentagon. "Graphs and combinatorics", Gener 2011, vol. 27, núm. 1, p. 47-60.
dc.identifier.citation	0911-0119
dc.identifier.citation	10.1007/s00373-010-0957-2
dc.identifier.uri	http://hdl.handle.net/2117/11669
dc.language.iso	eng
dc.relation	http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.0262v2.pdf
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
dc.subject	Pentagon
dc.subject	Hexagons
dc.subject	Ramsey theory
dc.subject	Discrete geometry
dc.subject	Convex geometry
dc.subject	Ramsey, Teoria de
dc.subject	Geometria discreta
dc.subject	Geometria convexa
dc.subject	Classificació AMS::52 Convex and discrete geometry::52C Discrete geometry
dc.subject	Classificació AMS::05 Combinatorics::05D Extremal combinatorics
dc.title	Every large point set contains many collinear points or an empty pentagon
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].

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