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Discrete & Computational Geometry

, Volume 19, Issue 3, pp 457–459 | Cite as

Note on the Erdos - Szekeres Theorem

  • G. Tóth
  • P. Valtr

Abstract.

Let g(n) denote the least integer such that among any g(n) points in general position in the plane there are always n in convex position. In 1935, P. Erdős and G. Szekeres showed that g(n) exists and \(2^{n-2}+1\le g(n)\le {2n-4\choose n-2}+1\) . Recently, the upper bound has been slightly improved by Chung and Graham and by Kleitman and Pachter. In this paper we further improve the upper bound to \(g(n)\le {2n-5\choose n-2}+2.\) <lsiheader> <onlinepub>26 June, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; <pdfname>19n3p457.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>yes <sectionname> </lsiheader>

Keywords

General Position Convex Position Szekeres Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • G. Tóth
    • 1
  • P. Valtr
    • 2
  1. 1.Courant Institute, NYU, 251 Mercer Street, New York, NY 10012, USA toth@cims.nyu.edu US
  2. 2.DIMACS Center, Rutgers University, Piscataway, NJ 08855, USA US

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