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

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Title:	Every large point set contains many collinear points or an empty pentagon
Author:	Wood, David; Por, Attila; Abel, Zachary; Ballinger, Brad; Bose, Prosenjit; Collette, Sébastien; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Kominers, Scott Duke; Langerman, Stefan
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
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].
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta -Pentagon -Hexagons -Ramsey theory -Discrete geometry -Convex geometry -Ramsey, Teoria de -Geometria discreta -Geometria convexa -Classificació AMS::52 Convex and discrete geometry::52C Discrete geometry -Classificació AMS::05 Combinatorics::05D Extremal combinatorics
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Document type:	Article - Published version Article
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