Contagious sets in random graphs

ANNALS OF APPLIED PROBABILITY, pp. 2675-2697, 2017.

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Abstract:

We consider the following activation process in undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least r active neighbors. A contagious set is a set whose activation results with the entire graph being active. Given a graph G, let m(G, r) be the minimal size ...More

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