Erdős–Szekeres theorem with forbidden order types

According to the classical Erdős–Szekeres theorem, every sufficiently large set of points in general position in the plane contains a large subset in convex position. Parallel to the Erdős–Hajnal problem in graph-Ramsey theory, we investigate how large such subsets must a configuration contain if it...

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Bibliographic Details
Published in:Journal of combinatorial theory. Series A 2006-04, Vol.113 (3), p.455-465
Main Authors: Károlyi, Gyula, Solymosi, József
Format: Article
Language:English
Subjects:
Combinatorial convexity
Erdős–Szekeres conjecture
Erdős–Szekeres theorem
Order type
Ramsey theory
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Summary:According to the classical Erdős–Szekeres theorem, every sufficiently large set of points in general position in the plane contains a large subset in convex position. Parallel to the Erdős–Hajnal problem in graph-Ramsey theory, we investigate how large such subsets must a configuration contain if it does not have any sub-configuration belonging to a fixed order type.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2005.04.006