Sharp threshold for percolation on expanders

Details Sharp threshold for percolation on expanders Sharp threshold for percolation on expanders

2009-06-19

arxiv.org/abs/0906.3657v1

Mathematics

Probability

14 pages

Scientific paper

We study the appearance of the giant component in random 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 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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