Every Large Point Set contains Many Collinear Points or an Empty Pentagon
- First Online:
- Cite this article as:
- Abel, Z., Ballinger, B., Bose, P. et al. Graphs and Combinatorics (2011) 27: 47. doi:10.1007/s00373-010-0957-2
- 142 Downloads
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].