Sharp concentration of the chromatic number on random graphsGn, p
- Cite this article as:
- Shamir, E. & Spencer, J. Combinatorica (1987) 7: 121. doi:10.1007/BF02579208
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The distribution of the chromatic number on random graphsGn, 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 thann1/6, it concentrates almost surely in five consecutive integers. Large deviation estimates for martingales are used in the proof.