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Keywords:

  • upper tails;
  • large deviations;
  • random graphs;
  • subgraph counts

Abstract

With ξkmath image the number of copies of Kk in the usual (Erdős-Rényi) random graph G(n,p), pn-2/(k-1) and η > 0, we show when k > 1

  • equation image

This is tight up to the value of the constant in the exponent. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012