English

Supercritical Site Percolation on the Hypercube: Small Components are Small

Probability 2022-04-12 v1 Combinatorics

Abstract

We consider supercritical site percolation on the dd-dimensional hypercube QdQ^d. We show that typically all components in the percolated hypercube, besides the giant, are of size O(d)O(d). 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}
}

Comments

6 pages

R2 v1 2026-06-24T10:44:26.464Z