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Poisson convergence and semi-induced properties of random graphs

1987; Cambridge University Press; Volume: 101; Issue: 2 Linguagem: Inglês

10.1017/s0305004100066664

1469-8064

Michał Karoński, Andrzej Ruciński,

Bayesian Methods and Mixture Models

Barbour [l] invented an ingenious method of establishing the asymptotic distribution of the number X of specified subgraphs of a random graph. The novelty of his method relies on using the first two moments of X only, despite the traditional method of moments that involves all moments of X (compare [ 8, 10, 11, 14 ]). He also adjusted that new method for counting isolated trees of a given size in a random graph. (For further applications of Barbour's method see [ 4 ] and [ 10 ].) The main goal of this paper is to show how this method can be extended to a general setting that enables us to derive asymptotic distributions of subsets of vertices of a random graph with various properties.