  Consider the triangle-free graph process, which starts from the empty graph
on $n$ vertices and a random ordering of the possible ${n \choose 2}$ edges;
the edges are added in this ordering provided the graph remains triangle free.
We will show that there exists a constant $c$ such that no copy of any fixed
finite triangle-free graph on $k$ vertices with at least $ck$ edges
asymptotically almost surely appears in the triangle-free graph process.
