Article

Combinatorica

, Volume 7, Issue 1, pp 121-129

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

  • Eli ShamirAffiliated withLeibniz Cent. for Research in Computer Science Inst. of Mathematics & Comp. Sci., Hebrew University
  • , Joel SpencerAffiliated withDepartment of Mathematics, State University of New York

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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.

AMS subject classification (1980)

05 C 15 60 C 05