On the probability of independent sets in random graphs

@article{Krivelevich2003OnTP,
  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},
  year={2003},
  volume={22},
  pages={1-14}
}
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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