More on an Erdős–Szekeres-Type Problem for Interior Points

Abstract

An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k≥1, let g(k) be the smallest integer such that every planar point set in general position with at least g(k) interior points has a convex subset of points with exactly k interior points of P. In this article, we prove that g(3)=9.