Electronic Journal of Probability

On percolation in random graphs with given vertex degrees

Svante Janson

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 5, 86-118.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819466

Digital Object Identifier
doi:10.1214/EJP.v14-603

Mathematical Reviews number (MathSciNet)
MR2471661

Zentralblatt MATH identifier
1189.60179

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 05C80: Random graphs [See also 60B20]

Keywords
random graph giant component k-core bootstrap percolation

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Janson, Svante. On percolation in random graphs with given vertex degrees. Electron. J. Probab. 14 (2009), paper no. 5, 86--118. doi:10.1214/EJP.v14-603. https://projecteuclid.org/euclid.ejp/1464819466


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