CaltechAUTHORS
  A Caltech Library Service

Finding Convex Sets Among Points in the Plane

Kleitman, D. and Pachter, L. (1998) Finding Convex Sets Among Points in the Plane. Discrete and Computational Geometry, 19 (3). pp. 405-410. ISSN 0179-5376. https://resolver.caltech.edu/CaltechAUTHORS:20170309-114305555

[img] PDF - Published Version
See Usage Policy.

76Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20170309-114305555

Abstract

Let g(n) denote the least value such that any g(n) points in the plane in general position contain the vertices of a convex n-gon. In 1935, Erdős and Szekeres showed that g(n) exists, and they obtained the bounds 2^(n−2) + 1 ≤ g(n) ≤ (^(2n−4)_(n−2)) + 1. Chung and Graham have recently improved the upper bound by 1; the first improvement since the original Erdős—Szekeres paper. We show that g(n) ≤ (^(2n−4)_(n−2)) + 7 − 2n.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1007/PL00009358DOIArticle
https://link.springer.com/article/10.1007/PL00009358PublisherArticle
http://rdcu.be/pXjgPublisherFree ReadCube access
ORCID:
AuthorORCID
Pachter, L.0000-0002-9164-6231
Additional Information:© 1998 Springer-Verlag. Received January 1, 1997, and in revised form June 6, 1997. We thank Géza Tóth and Pavel Valtr for contributing the lower bound construction. We also thank the referee for numerous helpful suggestions and comments.
Issue or Number:3
Record Number:CaltechAUTHORS:20170309-114305555
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170309-114305555
Official Citation:Kleitman, D. & Pachter, L. Discrete Comput Geom (1998) 19: 405. doi:10.1007/PL00009358
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74983
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:10 Mar 2017 03:15
Last Modified:24 Feb 2020 10:30

Repository Staff Only: item control page