Sharp concentration of the chromatic number on random graphs G_{n, p}

The distribution of the chromatic number on random graphs G_{n, p} is quite sharply concentrated. For fixed p it concentrates almost surely in √n ω(n) consecutive integers where ω(n) approaches infinity arbitrarily slowly. If the average degree pn is less than n^1/6, it concentrates almost surely in five consecutive integers. Large deviation estimates for martingales are used in the proof.