On Convex Decompositions of Points

Given a planar point set in general position, S, we seek a partition of the points into convex cells, such that the union of the cells forms a simple polygon, P, and every point from S is on the boundary of P. Let f(S) denote the minimum number of cells in such a partition of S. Let F(n) be defined as the maximum value of f(S) when S has n points. In this paper we show that ?(n - l)/4? ? F(n) ? ?(3n - 2)/5?.