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Every Large Point Set Contains Many Collinear Points or an Empty Pentagon
By: Zachary Abel, Brad Ballinger, Prosenjit Bose, Sébastien Collette, Vida Dujmović, Ferran Hurtado, Scott Duke Kominers, Stefan Langerman, Attila Pór and David Wood
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”... View Details