Sharp threshold for percolation on expanders
Itai Benjamini, Stephane Boucheron, Gábor Lugosi and Raphael Rossignol
Annals of Probability 2011.

Abstract

Westudytheappearanceofthegiantcomponentinrandom 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.

[Edit]