Convex Independent Subsets
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:
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© Springer-Verlag New York, Inc. 2002