The diamond-free process
Let 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 . We show that, with probability tending to 1 as , the final size of the graph produced is . 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. Random Struct. Alg., 45, 513551, 2014
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