, Volume 7, Issue 1, pp 35-38

First online:

Threshold functions

  • B. BollobásAffiliated withDepartment of Pure Mathematics, University of CambridgeDepartment of Mathematics, LSU
  • , A. G. ThomasonAffiliated withDepartment of Mathematics, LSUDepartment of Mathematics, University of Exeter

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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