The maximal running time of hypergraph bootstrap percolation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866915031715676160 |
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| author | Hartarsky, Ivailo Lichev, Lyuben |
| author_facet | Hartarsky, Ivailo Lichev, Lyuben |
| contents | We show that for every $r\ge 3$, the maximal running time of the $K^{r}_{r+1}$-bootstrap percolation in the complete $r$-uniform hypergraph on $n$ vertices $K_n^r$ is $Θ(n^r)$. This answers a recent question of Noel and Ranganathan in the affirmative, and disproves a conjecture of theirs. Moreover, we show that the prefactor is of the form $r^{-r} \mathrm{e}^{O(r)}$ as $r\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13489 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The maximal running time of hypergraph bootstrap percolation Hartarsky, Ivailo Lichev, Lyuben Combinatorics 05C35 (Primary), 05C65, 05D99 (Secondary) We show that for every $r\ge 3$, the maximal running time of the $K^{r}_{r+1}$-bootstrap percolation in the complete $r$-uniform hypergraph on $n$ vertices $K_n^r$ is $Θ(n^r)$. This answers a recent question of Noel and Ranganathan in the affirmative, and disproves a conjecture of theirs. Moreover, we show that the prefactor is of the form $r^{-r} \mathrm{e}^{O(r)}$ as $r\to\infty$. |
| title | The maximal running time of hypergraph bootstrap percolation |
| topic | Combinatorics 05C35 (Primary), 05C65, 05D99 (Secondary) |
| url | https://arxiv.org/abs/2208.13489 |