Bootstrap percolation on a generalized Hamming cube
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918407844134912 |
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| author | Zhu, Fengxing |
| author_facet | Zhu, Fengxing |
| contents | We consider the $r$-neighbor bootstrap percolation process on the graph with vertex set $V=\{0,1\}^n$ and edges connecting the pairs at Hamming distance $1,2,\dots,k$, where $k\ge 2$. We find asymptotics of the critical probability of percolation for $r=2,3$. In the deterministic setting, we obtain several results for the size of the smallest percolating set for $k\ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20982 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bootstrap percolation on a generalized Hamming cube Zhu, Fengxing Combinatorics We consider the $r$-neighbor bootstrap percolation process on the graph with vertex set $V=\{0,1\}^n$ and edges connecting the pairs at Hamming distance $1,2,\dots,k$, where $k\ge 2$. We find asymptotics of the critical probability of percolation for $r=2,3$. In the deterministic setting, we obtain several results for the size of the smallest percolating set for $k\ge 2$. |
| title | Bootstrap percolation on a generalized Hamming cube |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.20982 |