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Problems and Results around the Erdös-Szekeres Convex Polygon Theorem

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Discrete and Computational Geometry (JCDCG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2098))

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Abstract

Eszter Klein’s theorem claims that among any 5 points in the plane, no three collinear, there is the vertex set of a convex quadrilateral.An application of Ramsey’s theorem then yields the classical Erdös-Szekeres theorem [19]: For every integer n ≥ 3 there is an N0 such that, among any set of N ≥ N 0 points in general position in the plane, there is the vertex set of a convex n-gon. Let f(n) denote the smallest such number.

The authors gratefully acknowledge that they have been partially supported by Hungarian Research Grants OTKA T032452 and F030822, respectively.

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Author information

Authors and Affiliations

  1. Maths, University College London, UK

    Imre Bárány

  2. Rényi Institute, Budapest

    Imre Bárány

  3. Eötvös University, Budapest

    Gyula Károlyi

Authors
  1. Imre Bárány
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  2. Gyula Károlyi
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Editors and Affiliations

  1. Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokyo, 151-0063, Japan

    Jin Akiyama

  2. Department of Computer and Information Sciences, Ibaraki University, Hitachi, 316-8511, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido Shimizu-shi, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

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© 2001 Springer-Verlag Berlin Heidelberg

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Bárány, I., Károlyi, G. (2001). Problems and Results around the Erdös-Szekeres Convex Polygon Theorem. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_7

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  • DOI: https://doi.org/10.1007/3-540-47738-1_7

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  • Print ISBN: 978-3-540-42306-5

  • Online ISBN: 978-3-540-47738-9

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