The Happy End Theorem and Related Results

  • Pavel Valtr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8344)


The Erdös-Szekeres k-gon theorem [1] says that for any integer k ≥ 3 there is an integer n(k) such that any set of n(k) points in the plane, no three on a line, contains k points which are vertices of a convex k-gon. It is a classical result both in combinatorial geometry and in Ramsey theory. Sometimes it is called the Happy End(ing) Theorem (a name given by Paul Erdös), since George Szekeres later married Eszter Klein who proposed a question answered by the theorem.


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    Erdős, P., Szekeres, G.: A combinatorial problem in geometry. Compos. Math. 2, 463–470 (1935)Google Scholar
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    Erdős, P., Szekeres, G.: On some extremum problems in elementary geometry. Ann. Univ. Sci. Bp. Rolan do Eötvös Nomin., Sect. Math. 3/4, 53–62 (1960–1961)Google Scholar
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    Szekeres, G., Peters, L.: Computer solution to the 17-point Erdős-Szekeres problem. ANZIAM Journal 48, 151–164 (2006)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Pavel Valtr
    • 1
  1. 1.Department of Applied Mathematics and Institute for Theoretical Computer Science, Faculty of Mathematics and PhysicsCharles UniversityPraha 1Czech Republic

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