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arXiv · 0711.1713

Bondary-connectivity via graph theory

Adam Timar
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Abstract

We generalize theorems of Kesten and Deuschel-Pisztora about the connectedness of the exterior boundary of a connected subset of $\mathbb{Z}^d$, where "connectedness" and "boundary" are understood with respect to various graphs on the vertices of $\mathbb{Z}^d$. We provide simple and elementary proofs of their results. It turns out that the proper way of viewing these questions is graph theory, instead of topology.

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Adam Timar. 2007-11-12. Bondary-connectivity via graph theory. https://arxiv.org/abs/0711.1713

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