Asymptotic performance of the Grimmett-McDiarmid heuristic

Grimmett and McDiarmid suggested a simple heuristic for finding stable sets in random graphs. They showed that the heuristic finds a stable set of size $\sim {\log }_{2}n$ (with high probability) on a $G(n,1\mathrm{/}2)$ random graph. We determine the asymptotic distribution of the size of the stable set found by the algorithm.