Point Sets with Small Integer Coordinates and with Small Convex Polygons

Frank Duque, Ruy Fabila-Monroy, Carlos Hidalgo-Toscano

In 1935, Erdős and Szekeres proved that every set of $n$ points in general position in the plane contains the vertices of a convex polygon of $\frac{1}{2}{\log }_2(n)$ vertices. In 19…