Highly Influenced

# The perturbation method and triangle-free random graphs

@article{Wormald1996ThePM, title={The perturbation method and triangle-free random graphs}, author={Nicholas C. Wormald}, journal={Random Struct. Algorithms}, year={1996}, volume={9}, pages={253-269} }

- Published 1996 in Random Struct. Algorithms
DOI:10.1002/(SICI)1098-2418(199608/09)9:1/2%3C253::AID-RSA15%3E3.0.CO;2-O

When a discrete random variable in a discrete space is asymptotically Poisson, there is often a powerful method of estimating its distribution, by calculating the ratio of the probabilities of adjacent values of the variable. The versatility of this method is demonstrated by finding asymptotically the probability that a random graph has no triangles, provided the edge density is not too large. In particular, the probability that G ∈ G(n, p) has no triangles is asymptotic to exp(− 6p 3n3 + 14p… CONTINUE READING