Given a finite set S of points in the plane, a convex partition of S is a subdivision of the convex hull of S into nonoverlapping empty convex polygons with vertices in S. Let G(S) be the minimum m such that there exists a convex partition of S with at most m faces. Let F(n) be the maximum value of G(S) among all the sets of n points in the plane. It is known  that F(n) ≥ n + 2 for n ≥ 13. In this paper we show that, for n ≥ 4 F(n)> 12 n − 2. Als
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