Journal article

The phase transition in the configuration model

Abstract:

Let $G=G(d)$ be a random graph with a given degree sequence $d$, such as a random $r$-regular graph where $r\ge 3$ is fixed and $n=|G|\to\infty$. We study the percolation phase transition on such graphs $G$, i.e., the emergence as $p$ increases of a unique giant component in the random subgraph $G[p]$ obtained by keeping edges independently with probability $p$. More generally, we study the emergence of a giant component in $G(d)$ itself as $d$ varies. We show that a single method can be used...

Publication status:
Published

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Publisher copy:
10.1017/S0963548311000666

Authors

Journal:
Combinatorics, Probability and Computing 21 (2012), 265--299
Volume:
21
Issue:
1-2
Pages:
265-299
Publication date:
2011-04-04
DOI:
EISSN:
1469-2163
ISSN:
0963-5483
Source identifiers:
146889
Language:
English
Keywords:
Pubs id:
pubs:146889
UUID:
Local pid:
pubs:146889
Deposit date:
2013-02-20