An order-refined and generalized version of the Erdos-Szekeres theorem on convex polygons
Combinatorics
2007-05-23 v1 Metric Geometry
Abstract
The Erdos-Szekeres theorem states that for any natural k there is a natural number g(k) such that any set of at least g(k) points on a plane in general position contains a set of k points that are the extreme points of a convex polytope. We generalize and refine this theorem, having the general-position condition removed and a convex polygon defined as an ordered sequence of points such that the union of the edges of the polygon coincides with the boundary of its convex hull.
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Cite
@article{arxiv.math/0611802,
title = {An order-refined and generalized version of the Erdos-Szekeres theorem on convex polygons},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:math/0611802},
year = {2007}
}
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5 pages