Combinatorica

, Volume 7, Issue 1, pp 121–129

Sharp concentration of the chromatic number on random graphsGn, p

  • Eli Shamir
  • Joel Spencer
Article

DOI: 10.1007/BF02579208

Cite this article as:
Shamir, E. & Spencer, J. Combinatorica (1987) 7: 121. doi:10.1007/BF02579208

Abstract

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.

AMS subject classification (1980)

05 C 15 60 C 05 

Copyright information

© Akadémiai Kiadó 1987

Authors and Affiliations

  • Eli Shamir
    • 1
  • Joel Spencer
    • 2
  1. 1.Leibniz Cent. for Research in Computer Science Inst. of Mathematics & Comp. Sci.Hebrew UniversityJerusalem Givet RamIsrael
  2. 2.Department of MathematicsState University of New YorkStone BrookUSA

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