How sharp is the concentration of the chromatic number?
The chromatic number of a random graph was determined. If the probability is small then the concentration of the chromatic number is even sharper. These concentration results did not improve at all the known bounds in the chromatic number. The results show that chromatic number is very sharply concentrated about a known value.
Combinatorics Probability and Computing
Bollobás, B. (2004). How sharp is the concentration of the chromatic number?. Combinatorics Probability and Computing, 13 (1), 115-117. https://doi.org/10.1017/S0963548303006060