(1) Department of Pure Mathematics, University of Cambridge, Cambridge, England;(2) Department of Mathematics, LSU, Baton Rouge, LA, USA;(3) Department of Mathematics, University of Exeter, Exeter, England
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. First author supported by NSF grant MCS 8104854