Convexly independent sets

Combinatorica volume 10, pages195–202(1990)Cite this article

Abstract

A family of pairwise disjoint compact convex sets is called convexly independent, if none of its members is contained in the convex hull of the union of the other members of the family. The main result of the paper gives an upper bound for the maximum cardinalityh(k, n) of a family ℱ of mutually disjoint compact convex sets such that any subfamily of at mostk members of ℱ is convexly independent, but no subfamily of sizen is.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

US$ 39.95

Tax calculation will be finalised during checkout.

References

  1. [1]

    T. Bisztriczky, andG. Fejes Tóth: A generalization of the Erdős-Szekeres convexn-gon theorem,J. reine angew. Math. 395(1989) 167–170.

    Google Scholar 

  2. [2]

    T. Bisztriczky, andG. Fejes Tóth: Nine convex sets determine a pentagon with convex sets as vertices,Geometriae Dedicata 31(1989) 89–104.

    Google Scholar 

  3. [3]

    P. ErdőS, andG. Szekeres: A combinatorical problem in geometry,Comp. Math.,2 (1935), 463–470.

    Google Scholar 

  4. [4]

    P. Erdős, andG. Szekeres: On some extremum problems in elementary geometry,Ann. Univ. Sci. Budapest, Eötvös Sect. Math.,3–4 (1960–61), 53–62.

    Google Scholar 

  5. [5]

    R. L. Graham, B. L. Rothschild, andJ. H. Spencer:Ramsey theory, Wiley, New York (1980).

    Google Scholar 

Download references

Author information

Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, 2500 University Dr. N. W. Calgary, T2N 1N4, Alberta, Canada

    T. Bisztriczky

  2. Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, H-1364, Budapest, Hungary

    G. Fejes Tóth

Authors
  1. T. Bisztriczky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Fejes Tóth
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bisztriczky, T., Tóth, G.F. Convexly independent sets. Combinatorica 10, 195–202 (1990). https://doi.org/10.1007/BF02123010

Download citation

AMS subject classification (1980)

  • 52 A 10
  • 05 A 17