  The random greedy algorithm for constructing a large partial
Steiner-Triple-System is defined as follows. We begin with a complete graph on
$n$ vertices and proceed to remove the edges of triangles one at a time, where
each triangle removed is chosen uniformly at random from the collection of all
remaining triangles. This stochastic process terminates once it arrives at a
triangle-free graph. In this note we show that with high probability the number
of edges in the final graph is at most $ O\big( n^{7/4}\log^{5/4}n \big) $.
