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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.
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A 2012 study studied this question.
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