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A simple branching process approach to the phase transition in $G_{n,p}$

Abstract:
It is well known that the branching process approach to the study of the random graph $G_{n,p}$ gives a very simple way of understanding the size of the giant component when it is fairly large (of order $\Theta(n)$). Here we show that a variant of this approach works all the way down to the phase transition: we use branching process arguments to give a simple new derivation of the asymptotic size of the largest component whenever $(np-1)^3n\to\infty$.
Publication status:
Published

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Journal:
Electronic Journal of Combinatorics
Volume:
19
Issue:
4
Pages:
P21
Publication date:
2012-07-26
EISSN:
1077-8926
ISSN:
1077-8926
Source identifiers:
344409
Language:
English
Keywords:
Pubs id:
pubs:344409
UUID:
uuid:13b7e4a0-c4f3-43ed-96d6-01bd06cf26b9
Local pid:
pubs:344409
Deposit date:
2013-11-17

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