Resumen de Sharp threshold for percolation on expanders

Itai Benjamini, Stéphane Boucheron, Gábor Lugosi, Raphaël Rossignol

• We study the appearance of the giant component in random subgraphs of a given large finite graph G = (V, E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c ∈ ]0, 1[, the property that the random subgraph contains a giant component of size c|V| has a sharp threshold.