Open Access
2009 On percolation in random graphs with given vertex degrees
Svante Janson
Author Affiliations +
Electron. J. Probab. 14: 86-118 (2009). DOI: 10.1214/EJP.v14-603


We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for random graphs with given vertex degrees. This is used to study existence of giant component and existence of k-core. As a variation of the latter, we study also bootstrap percolation in random regular graphs. We obtain both simple new proofs of known results and new results. An interesting feature is that for some degree sequences, there are several or even infinitely many phase transitions for the k-core.


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Svante Janson. "On percolation in random graphs with given vertex degrees." Electron. J. Probab. 14 86 - 118, 2009.


Accepted: 20 January 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1189.60179
MathSciNet: MR2471661
Digital Object Identifier: 10.1214/EJP.v14-603

Primary: 60C05
Secondary: 05C80

Keywords: Bootstrap percolation , Giant component , k-core , random graph

Vol.14 • 2009
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