On percolation in random graphs with given vertex degrees
Svante Janson, Uppsala University
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.
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