Supercritical Site Percolation on the Hypercube: Small Components are Small
Probability
2022-04-12 v1 Combinatorics
Abstract
We consider supercritical site percolation on the -dimensional hypercube . We show that typically all components in the percolated hypercube, besides the giant, are of size . This resolves a conjecture of Bollob\'as, Kohayakawa, and {\L}uczak from 1994.
Keywords
Cite
@article{arxiv.2204.05074,
title = {Supercritical Site Percolation on the Hypercube: Small Components are Small},
author = {Sahar Diskin and Michael Krivelevich},
journal= {arXiv preprint arXiv:2204.05074},
year = {2022}
}
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6 pages