Supercritical Site Percolation on the Hypercube: Small Components are Small

preprint2022arXivOpen access

We consider supercritical site percolation on the $d$ -dimensional hypercube $Q^d$ . We show that typically all components in the percolated hypercube, besides the giant, are of size $O(d)$ . This resolves a conjecture of Bollobás, Kohayakawa, and Łuczak from 1994.

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Supercritical Site Percolation on the Hypercube: Small Components are Small

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