A central limit theorem for decomposable random variables with applications to random graphs

@article{Barbour1989ACL,
title={A central limit theorem for decomposable random variables with applications to random graphs},
author={Andrew D. Barbour and Michal Karonski and Andrzej Rucinski},
journal={J. Comb. Theory, Ser. B},
year={1989},
volume={47},
pages={125-145}
}

The application of Stein’s method of obtaining rates of convergence to the normal distribution is illustrated in the context of random graph theory. Problems which exhibit a dissociated structure and problems which do not are considered. Results are obtained for the number of copies of a given graph G in K(n, p), for the number of induced copies of G, for the number of isolated trees of order k > 2, for the number of vertices of degree d> 1, and for the number of isolated vertices.