Expansion properties of a random regular graph after random vertex deletions

We investigate the following vertex percolation process. Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p = n- and = (n) is bounded away from 0. We show that a.a.s. the resulting graph has a connected component of size n - o(n) which is an expander, and all other components are trees of bounded size. Sharper results are obtained with extra conditions on . These results have an application to the cost of repairing a certain peer-to-peer network after random failures of nodes.

• Type: Journal
• Year: 2008
• Where: EJC
• Authors: Catherine S. Greenhill, Fred B. Holt, Nicholas C. Wormald
• Keywords: Connected Component, Constant Degree, EJC 2007, EJC 2008, Information Technology, Random Regular Graph