Combinatorica

, Volume 11, Issue 1, pp 45–54 | Cite as

The chromatic number of random graphs

  • Tomasz Łuczak
Article

Abstract

Let χ(G(n, p)) denote the chromatic number of the random graphG(n, p). We prove that there exists a constantd0 such that fornp(n)>d0,p(n)→0, the probability that
$$\frac{{np}}{{2 log np}}\left( {1 + \frac{{\log log np - 1}}{{\log np}}} \right)< \chi (G(n,p))< \frac{{np}}{{2 log np}}\left( {1 + \frac{{30 \log \log np}}{{\log np}}} \right)$$
tends to 1 asn→∞.

AMS subject classification (1991)

05 C 80 05 C 15 

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References

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    B. Bollobás: The chromatic number of random graphs,Combinatorica,8 (1988), 49–56.Google Scholar
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    E. Shamir, andJ. Spencer: Sharp concentration of the chromatic number on random graphsG n, p,Combinatorica,7 (1987), 124–129Google Scholar

Copyright information

© Akadémiai Kiadó 1991

Authors and Affiliations

  • Tomasz Łuczak
    • 1
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaUSA

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