Finding Convex Sets in Convex Position |
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Authors: | Géza Tóth |
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Institution: | DIMACS Center, Rutgers University and Rényi Intitute of Mathematics, Hungarian Academy of Sciences; H–1364 Budapest, P.O. Box 127, Hungary; E-mail: geza@renyi.hu, HU
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Abstract: | Let F{\cal{F}} denote a family of pairwise disjoint convex sets in the plane. F{\cal{F}} is said to be in convex position, if none of its members is contained in the convex hull of the union of the others. For any fixed k 3 5k\ge5, we give a linear upper bound on Pk(n)P_k(n), the maximum size of a family F{\cal{F}} with the property that any k members of F{\cal{F}} are in convex position, but no n are. |
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