The random greedy algorithm for constructing a 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 thisnote we show that with high probability the number of edges in the final graph is at most n~(7/4+o(1)).
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