Supercritical Site Percolation on the Hypercube: Small Components are Small
Abstract
We consider supercritical site percolation on the d-dimensional hypercube Qd. We show that typically all components in the percolated hypercube, besides the giant, are of size O(d). This resolves a conjecture of Bollob\'as, Kohayakawa, and uczak from 1994.
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