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

par Abel, Z.;Ballinger, Brad;Bose, Prosenjit ;Collette, Sébastien ;Dujmović, Vida V.;Hurtado, Ferran ;Kominers, S.D.;Langerman, Stefan ;Pór, A.;Wood, David
Référence Graphs and combinatorics, 27, 1, page (47-60)
Publication Publié, 2010

Article révisé par les pairs

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Résumé :

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]. © 2010 Springer.