Convex Independent Subsets

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


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:


Convex Hull General Position Finite Point Convex Position Good Quantitative Result 
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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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