Every Large Point Set contains Many Collinear Points or an Empty Pentagon
Combinatorics
2011-01-04 v2 Computational Geometry
Abstract
We prove the following generalised empty pentagon theorem: for every integer , 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 K\'ara, P\'or, and Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005].
Cite
@article{arxiv.0904.0262,
title = {Every Large Point Set contains Many Collinear Points or an Empty Pentagon},
author = {Zachary Abel and Brad Ballinger and Prosenjit Bose and Sébastien Collette and Vida Dujmović and Ferran Hurtado and Scott D. Kominers and Stefan Langerman and Attila Pór and David R. Wood},
journal= {arXiv preprint arXiv:0904.0262},
year = {2011}
}