The chromatic number of random graphs


Let χ(G(n, p)) denote the chromatic number of the random graphG(n, p). We prove that there exists a constantd 0 such that fornp(n)>d 0,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→∞.

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Łuczak, T. The chromatic number of random graphs. Combinatorica 11, 45–54 (1991).

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AMS subject classification (1991)

  • 05 C 80
  • 05 C 15