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

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10.1007/s00373-010-0957-2
 
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Cita com:
hdl:2117/11669

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Wood, David
Por, Attila
Abel, Zachary
Ballinger, Brad
Bose, Prosenjit
Collette, Sébastien
Dujmovic, Vida
Hurtado Díaz, Fernando AlfredoMés informacióMés informació
Kominers, Scott Duke
Langerman, Stefan
Document typeArticle
Defense date2011-01
Rights accessRestricted access - publisher's policy
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
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].
CitationAbel, 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. 
URIhttp://hdl.handle.net/2117/11669
DOI10.1007/s00373-010-0957-2
ISSN0911-0119
Publisher versionhttp://arxiv.org/PS_cache/arxiv/pdf/0904/0904.0262v2.pdf
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  • DCCG - Grup de recerca en geometria computacional, combinatoria i discreta - Articles de revista [85]
  • Departament de Matemàtiques - Articles de revista [3.102]
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