  Let K_4^- denote the diamond graph, formed by removing an edge from the
complete graph K_4. 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 K_4^-. We show that, with probability tending to 1 as $n \to
\infty$, the final size of the graph produced is $\Theta(\sqrt{\log(n)} \cdot
n^{3/2})$. Our analysis also suggests that the graph produced after i edges are
added resembles the random graph, with the additional condition that the edges
which do not lie on triangles form a random-looking subgraph.
