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

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

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