$H$-percolation with a random $H$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917081702727680 |
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| author | Bartha, Zsolt Kolesnik, Brett Kronenberg, Gal |
| author_facet | Bartha, Zsolt Kolesnik, Brett Kronenberg, Gal |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_03663 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $H$-percolation with a random $H$ Bartha, Zsolt Kolesnik, Brett Kronenberg, Gal Combinatorics Probability 05C35, 05C80, 05C99, 60K35, 68Q80 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. |
| title | $H$-percolation with a random $H$ |
| topic | Combinatorics Probability 05C35, 05C80, 05C99, 60K35, 68Q80 |
| url | https://arxiv.org/abs/2312.03663 |