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Poisson convergence and semi-induced properties of random graphs

Published online by Cambridge University Press:  24 October 2008

Michał Karoński  and
Andrzej Ruciński
Michał Karoński
Affiliation:
Institute of Mathematics, Adam Mickiewicz University, Poznań, Poland
Andrzej Ruciński
Affiliation:
Institute of Mathematics, Adam Mickiewicz University, Poznań, Poland
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 2 , March 1987 , pp. 291 - 300
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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