, Volume 7, Issue 1, pp 35–38

Threshold functions

  • B. Bollobás
  • A. G. Thomason


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.

AMS subject classification (1980)

60 C 05 05 C 30 


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  1. [1]
    B. Bollobás,Random Graphs, Academic Press, London, 1985.Google Scholar
  2. [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. [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

Copyright information

© Akadémiai Kiadó 1987

Authors and Affiliations

  • B. Bollobás
    • 1
    • 2
  • A. G. Thomason
    • 2
    • 3
  1. 1.Department of Pure MathematicsUniversity of CambridgeCambridgeEngland
  2. 2.Department of MathematicsLSUBaton RougeUSA
  3. 3.Department of MathematicsUniversity of ExeterExeterEngland

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