A subset of a finite set of points in the plane is called an empty convex polygon or a hole if it forms the set of vertices of a convex polygon whose interior contains no points of the set. Let  be the smallest integer such that any set of  points in the plane, no three collinear, contains a -hole for every  where the holes are pairwise disjoint. In this paper, we prove that

convex position, convex hull, empty convex polygon, hole, disjoint.