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arXiv · 2312.03663

$H$-percolation with a random $H$

Zsolt Bartha·Brett Kolesnik·Gal Kronenberg
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Abstract

In $H$-percolation, we start with an Erdős--Rényi graph ${\mathcal G}_{n,p}$ and then iteratively add edges that complete copies of $H$. The process percolates if all edges missing from ${\mathcal G}_{n,p}$ are eventually added. We find the critical threshold $p_c$ when $H={\mathcal G}_{k,1/2}$ is uniformly random, solving a problem of Balogh, Bollobás and Morris.

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Zsolt Bartha, Brett Kolesnik, Gal Kronenberg. 2023-12-06. $H$-percolation with a random $H$. https://doi.org/10.1214/24-ecp602

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