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# 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} }

- Published 2003 in Random Struct. Algorithms
DOI:10.1002/rsa.10063

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