Large Finite Point Sets Have 4 Collinear Points or a 6-Clique

Abstract

We prove that every finite point set of size at least $10^{11055931}$ has four collinear points or six points that pairwise see each other. This resolves the first open case of the big-line-big-clique conjecture of Kára, Pór, and Wood.

arXiv comment7 pages