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:
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© 2002 Springer-Verlag New York, Inc.
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Matoušek, J. (2002). Convex Independent Subsets. In: Matoušek, J. (eds) Lectures on Discrete Geometry. Graduate Texts in Mathematics, vol 212. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0039-7_3
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DOI: https://doi.org/10.1007/978-1-4613-0039-7_3
Publisher Name: Springer, New York, NY
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