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Keywords:

  • H-free process;
  • random greedy algorithm;
  • differential equations method

Abstract

Let inline image denote the diamond graph, formed by removing an edge from the complete graph K4. We consider the following random graph process: starting with n isolated vertices, add edges uniformly at random provided no such edge creates a copy of inline image. We show that, with probability tending to 1 as inline image, the final size of the graph produced is inline image. Our analysis also suggests that the graph produced after i edges are added resembles the uniform random graph, with the additional condition that the edges which do not lie on triangles form a random-looking subgraph. © 2013 Wiley Periodicals, Inc.