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arXiv · 0906.3657

Sharp threshold for percolation on expanders

Itai Benjamini·Stéphane Boucheron·Gábor Lugosi·Raphaël Rossignol
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Abstract

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 in ]0,1[, the property that the random subgraph contains a giant component of size c|V| has a sharp threshold.

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Itai Benjamini, Stéphane Boucheron, Gábor Lugosi, Raphaël Rossignol. 2009-06-19. Sharp threshold for percolation on expanders. https://doi.org/10.1214/10-aop610

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