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2008

Expansion properties of a random regular graph after random vertex deletions

8 years 3 months ago
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.
Catherine S. Greenhill, Fred B. Holt, Nicholas C.
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where EJC
Authors Catherine S. Greenhill, Fred B. Holt, Nicholas C. Wormald
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