Supercritical site percolation on the hypercube: small components are small
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Published:2022-11-25
Issue:3
Volume:32
Page:422-427
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ISSN:0963-5483
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Container-title:Combinatorics, Probability and Computing
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language:en
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Short-container-title:Combinator. Probab. Comp.
Author:
Diskin Sahar,Krivelevich Michael
Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Reference8 articles.
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