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Some remarks about extreme degrees in a random graph

Published online by Cambridge University Press:  24 October 2008

Zbigniew Palka
Zbigniew Palka
Affiliation:
Institute of Mathematics, A. Mickiewicz University, Poznań, Poland
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Extract

Let Kn, p be a random subgraph of a complete graph Kn obtained by removing edges, each with the same probability q = 1 – p, independently of all other edges (i.e. each edge remains in Kn, p with probability p). Very detailed results devoted to probability distributions of the number of vertices of a given degree, as well as of the extreme degrees of Kn, p, have already been obtained by many authors (see e.g. [l]–[5], [7]–[9]). A similar subject for other models of random graphs has been investigated in [10]–[13], The aim of this note is to give some supplementary information about the distribution of the ith smallest (i ≥ 1 is fixed) and the ith largest degree in a sparse random graph Kn, p, i.e. when p = p(n) = o(1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 1 , July 1986 , pp. 167 - 174
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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