Discrete & Computational Geometry

, Volume 19, Issue 3, pp 437–445 | Cite as

A Generalization of the Erdos - Szekeres Theorem to Disjoint Convex Sets

  • J. Pach
  • G. Tóth

Abstract.

Let F denote a family of pairwise disjoint convex sets in the plane. F is said to be in convex position if none of its members is contained in the convex hull of the union of the others. For any fixed k≥ 3 , we estimate P k (n) , the maximum size of a family F with the property that any k members of F are in convex position, but no n are. In particular, for k=3 , we improve the triply exponential upper bound of T. Bisztriczky and G. Fejes Tóth by showing that P 3 (n) < 16 n . <lsiheader> <onlinepub>26 June, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; <pdfname>19n3p437.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>yes <sectionname> </lsiheader>

Keywords

Convex Hull Maximum Size Pairwise Disjoint Disjoint Convex Pairwise Disjoint Convex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© 1998 Springer-Verlag New York Inc.

Authors and Affiliations

  • J. Pach
    • 1
  • G. Tóth
    • 1
  1. 1.Courant Institute, NYU, 251 Mercer Street, New York, NY 10012, USA and Mathematical Institute, Hungarian Academy of Sciences, Pf 127, H-1364 Budapest, Hungary \{pach,geza\}@math-inst.huUS

Personalised recommendations