Electronic Journal of Probability
- Electron. J. Probab.
- Volume 14 (2009), paper no. 5, 86-118.
On percolation in random graphs with given vertex degrees
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.
Electron. J. Probab., Volume 14 (2009), paper no. 5, 86-118.
Accepted: 20 January 2009
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
This work is licensed under aCreative Commons Attribution 3.0 License.
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