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

@article{Abel2009EveryLP,
  title={Every Large Point Set contains Many Collinear Points or an Empty Pentagon},
  author={Zachary Abel and B. Ballinger and P. Bose and S{\'e}bastien Collette and V. Dujmovic and F. Hurtado and S. Kominers and S. Langerman and A. P{\'o}r and D. Wood},
  journal={Graphs and Combinatorics},
  year={2009},
  volume={27},
  pages={47-60}
}
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]. 
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