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Convex Independent Subsets

  • Jiří Matoušek
Part of the Graduate Texts in Mathematics book series (GTM, volume 212)

Abstract

Here we consider geometric Ramsey-type results about finite point sets in the plane. Ramsey-type theorems are generally statements of the following type: Every sufficiently large structure of a given type contains a “regular” substructure of a prescribed size. In the forthcoming Erdős-Szekeres theorem (Theorem 3.1.3), the “structure of a given type” is simply a finite set of points in general position in R2, and the “regular substructure” is a set of points forming the vertex set of a convex polygon, as is indicated in the picture:

Keywords

Convex Hull General Position Finite Point Convex Position Good Quantitative Result 
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.

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Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Jiří Matoušek
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic

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