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Poisson convergence and semi-induced properties of random graphs

Published online by Cambridge University Press:  24 October 2008

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

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
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

[1]Barbour, A. D.. Poisson convergence and random graphs. Math. Proc. Cambridge Philos. Soc. 92 (1982), 349359.CrossRefGoogle Scholar
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[10]Karoński, M.. Balanced Subgraphs of Large Random Graphs (Adam Mickiewicz University Press, Poznań, 1984).Google Scholar
[11]Karoński, M. and Ruciński, A.. On the number of strictly balanced subgraphs of a random graph. In Graph Theory, Łagów, 1981, Lecture Notes in Math. 1018 (Springer-Verlag, 1983), 7983.Google Scholar
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