On a partition into convex polygons
Discrete Applied Mathematics
Computing the largest empty convex subset of a set of points
SCG '85 Proceedings of the first annual symposium on Computational geometry
Partitioning point sets in space into disjoint convex polytopes
Computational Geometry: Theory and Applications
Problems and Results around the Erdös-Szekeres Convex Polygon Theorem
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
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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 驴(n - l)/4驴 驴 F(n) 驴 驴(3n - 2)/5驴.