Skip to main content
SpringerLink
Log in

Threshold functions

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

It is shown that every non-trivial monotone increasing property of subsets of a set has a threshold function. This generalises a number of classical results in the theory of random graphs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. Bollobás,Random Graphs, Academic Press, London, 1985.

    Google Scholar 

  2. G. Katona, A theorem of finite sets, in:Theory of Graphs (P. Erdös and G. Katona, eds), Academic Press, New York, 1968, 187–207.

    Google Scholar 

  3. J. B. Kruskal, The number of simplices in a complex, in:Math. Optimization Techniques, Univ. Calif. Press, Berkeley and Los Angeles, 1963, 251–278.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Pure Mathematics, University of Cambridge, Cambridge, England

    B. Bollobás

  2. Department of Mathematics, LSU, Baton Rouge, LA, USA

    B. Bollobás & A. G. Thomason

  3. Department of Mathematics, University of Exeter, Exeter, England

    A. G. Thomason

Authors
  1. B. Bollobás
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. G. Thomason
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

First author supported by NSF grant MCS 8104854

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bollobás, B., Thomason, A.G. Threshold functions. Combinatorica 7, 35–38 (1987). https://doi.org/10.1007/BF02579198

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579198

AMS subject classification (1980)

Search

Navigation