We prove the following generalised empty pentagon theorem: for every integer l 2, every sufficiently large set of points in the plane contains ̀ 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].

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Conference 21st Annual Canadian Conference on Computational Geometry, CCCG 2009
Citation
Abel, Z. (Zachary), Ballinger, B. (Brad), Bose, P, Collette, S. (Sébastien), Dujmović, V, Hurtado, F. (Ferran), … Wood, D. (2009). Every large point set contains many collinear points or an empty pentagon. Presented at the 21st Annual Canadian Conference on Computational Geometry, CCCG 2009.