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On the Concentration of the Chromatic Number of Random Graphs

On the Concentration of the Chromatic Number of Random Graphs

Shamir and Spencer proved in the 1980s that the chromatic number of the binomial random graph $G_{n,p}$ is concentrated in an interval of length at most $\omega\sqrt{n}$, and in the 1990s Alon showed that an interval of length $\omega\sqrt{n}/\log n$ suffices for constant edge-probabilities $p\in (0,1)$. We prove a similar …