Sharp threshold for percolation on expanders ## AbstractWestudytheappearanceofthegiantcomponentinrandom subgraphs of a given 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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