Bigraph percolation problems
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913505186152448 |
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| author | Coregliano, Leonardo N. |
| author_facet | Coregliano, Leonardo N. |
| contents | A bigraph $G$ is weakly norming if the $e(G)$th root of the density of $G$ in $\lvert W\rvert$ is a norm in the space of bounded measurable functions $W\colonΩ\timesΛ\to\mathbb{R}$. The only known technique, due to Conlon--Lee, to show that a bigraph $G$ is weakly norming is to present a cut-percolation sequence of $G$.
In this paper, we identify a key obstacle for cut-percolation, which we call fold-stability and we show that existence of a cut-percolating of a bigraph $G$ is equivalent to non-existence of non-monochromatic fold-stable colorings of the edges of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14257 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bigraph percolation problems Coregliano, Leonardo N. Combinatorics Primary: 05C70. Secondary: 05C60, 05C25, 05C50 A bigraph $G$ is weakly norming if the $e(G)$th root of the density of $G$ in $\lvert W\rvert$ is a norm in the space of bounded measurable functions $W\colonΩ\timesΛ\to\mathbb{R}$. The only known technique, due to Conlon--Lee, to show that a bigraph $G$ is weakly norming is to present a cut-percolation sequence of $G$. In this paper, we identify a key obstacle for cut-percolation, which we call fold-stability and we show that existence of a cut-percolating of a bigraph $G$ is equivalent to non-existence of non-monochromatic fold-stable colorings of the edges of $G$. |
| title | Bigraph percolation problems |
| topic | Combinatorics Primary: 05C70. Secondary: 05C60, 05C25, 05C50 |
| url | https://arxiv.org/abs/2408.14257 |