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Keywords:

  • Random graphs;
  • regular graphs;
  • sharp threshold

Abstract

In this paper it is proved that in the random graph model G(n,p), the property of containing a k -regular subgraph, has a sharp threshold for k ≥ 3. It is also shown how to use similar methods to prove, quite easily, the (known fact of) sharpness of having a non empty k -core for k ≥ 3. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 42, 509–519, 2013