On the concentration of the chromatic number of random graphs
Abstract
Let 0<p<1 be fixed. Shamir and Spencer proved in the 1980s that the chromatic number of a random graph in G(n,p) is concentrated in an interval of length about n1/2. In this explanatory note, we give a proof of a result due due Noga Alon, showing that the chromatic number is concentrated in an interval of length about n1/2/log n.
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