On the Existente of a Point Subset with 4 or 5 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 h(k) be the smallest integer such that every set of points in the plane, no three collinear, containing at least h(k) interior points has a subset of points containing k or k + 1 interior points. We proved that h(3) =3 in an earlier paper. In this paper we prove that h(4) = 7.