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arXiv · 2408.14257

Bigraph percolation problems

Leonardo N. Coregliano
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Abstract

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 $G$.

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Leonardo N. Coregliano. 2024-09-17. Bigraph percolation problems. https://arxiv.org/abs/2408.14257

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