On the probability of independent sets in random graphs

  title={On the probability of independent sets in random graphs},
  author={Michael Krivelevich and Benny Sudakov and Van H. Vu and Nicholas C. Wormald},
  journal={Random Struct. Algorithms},
Let k be the asymptotic value of the independence number of the random graph G(n, p). We prove that if the edge probability p(n) satisfies p(n) À n−2/5 ln n then the probability that G(n, p) does not contain an independent set set of size k−c, for some absolute constant c > 0, is at most exp{−cn2/(k4p)}. We also show that the obtained exponent is tight up to logarithmic factors, and apply our result to obtain new bounds on the choice number of random graphs. We also discuss a general setting… CONTINUE READING

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Publications referenced by this paper.
Showing 1-10 of 25 references

Choosability in graphs

  • P. Erdős, A. L. Rubin, H. Taylor
  • Proc. West Coast Conf. on Combinatorics, Graph…
  • 1979
Highly Influential
4 Excerpts

Random graphs

  • S. Janson, T. Ã Luczak, A. Ruciński
  • Wiley, New York
  • 2000

Wormald , Random regular graphs of high degree

  • B. Sudakov M. Krivelevich, V. H. Vu, C. N.
  • Random Struct Alg
  • 2000

Coloring the verti es of a graph in pres ribed olors ( in Russian ) , Diskret . Analiz . No . 29 , Metody Diskret

  • J. Spen er
  • Anal . v . Teorii Kodov i Shem
  • 1994

Coloring the vertices of a graph in prescribed colors ( in Russian ) , Diskret Anal 29

  • V. G. Vizing
  • Met Diskret Anal Teor Kodov Shem
  • 1994

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