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arXiv · 0904.0262

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

Zachary Abel·Brad Ballinger·Prosenjit Bose·Sébastien Collette·Vida Dujmović·Ferran Hurtado·Scott D. Kominers·Stefan Langerman·Attila Pór·David R. Wood
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Abstract

We prove the following generalised empty pentagon theorem: for every integer $\ell \geq 2$, every sufficiently large set of points in the plane contains $\ell$ 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 [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005].

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Zachary Abel, Brad Ballinger, Prosenjit Bose, Sébastien Collette, Vida Dujmović, Ferran Hurtado, Scott D. Kominers, Stefan Langerman, Attila Pór, David R. Wood. 2009-04-24. Every Large Point Set contains Many Collinear Points or an Empty Pentagon. https://doi.org/10.1007/s00373-010-0957-2

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