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


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>


Convex Hull Maximum Size Pairwise Disjoint Disjoint Convex Pairwise Disjoint Convex 
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Copyright information

© Springer-Verlag New York Inc. 1998

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

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