Finding sets of points without empty convex 6-gons (Q1864134)

The author investigates a problem posed by Erdős which asks whether every large enough set of points in general position in the plane contains six points that form a convex \(6\)-gon without any points from the set in its interior. The author presents a fast incremental algorithm with which he was able to find a set of \(29\) points in the plane in general position which does not contain empty \(6\)-gons. In addition, using results obtained by the algorithm, a number of observations and conjectures are formulated about the possible structure of sets of points without empty convex \(6\)-gons.