Sharp concentration of the chromatic number on random graphsG n, p

Abstract

The distribution of the chromatic number on random graphsG n, p is quite sharply concentrated. For fixedp it concentrates almost surely in √n ω(n) consecutive integers where ω(n) approaches infinity arbitrarily slowly. If the average degreepn is less thann 1/6, it concentrates almost surely in five consecutive integers. Large deviation estimates for martingales are used in the proof.

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Shamir, E., Spencer, J. Sharp concentration of the chromatic number on random graphsG n, p . Combinatorica 7, 121–129 (1987). https://doi.org/10.1007/BF02579208

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AMS subject classification (1980)

  • 05 C 15
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