Before revision:  In the dense graph model, a similar picture is long known (Alon, Fisher , Krivelevich, Szegedy, Combinatoria 2000), despite the very different nature of the two models.
After revision:  In the dense graph model, a similar picture is long known (Alon, Fisher , Krivelevich, Szegedy, Combinatorica 2000), despite the very different nature of the two models.