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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.
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