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Finding Convex Sets Among Points in the Plane

Kleitman, D. and Pachter, L. (1998) Finding Convex Sets Among Points in the Plane. Discrete and Computational Geometry, 19 (3). pp. 405-410. ISSN 0179-5376. doi:10.1007/PL00009358.

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Let g(n) denote the least value such that any g(n) points in the plane in general position contain the vertices of a convex n-gon. In 1935, Erdős and Szekeres showed that g(n) exists, and they obtained the bounds 2^(n−2) + 1 ≤ g(n) ≤ (^(2n−4)_(n−2)) + 1. Chung and Graham have recently improved the upper bound by 1; the first improvement since the original Erdős—Szekeres paper. We show that g(n) ≤ (^(2n−4)_(n−2)) + 7 − 2n.

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Pachter, L.0000-0002-9164-6231
Additional Information:© 1998 Springer-Verlag. Received January 1, 1997, and in revised form June 6, 1997. We thank Géza Tóth and Pavel Valtr for contributing the lower bound construction. We also thank the referee for numerous helpful suggestions and comments.
Issue or Number:3
Record Number:CaltechAUTHORS:20170309-114305555
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Official Citation:Kleitman, D. & Pachter, L. Discrete Comput Geom (1998) 19: 405. doi:10.1007/PL00009358
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74983
Deposited By: George Porter
Deposited On:10 Mar 2017 03:15
Last Modified:15 Nov 2021 16:29

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