Bondary-connectivity via graph theory

Details Bondary-connectivity via graph theory Bondary-connectivity via graph theory

2007-11-12

arxiv.org/abs/0711.1713v2

Mathematics

Probability

8 pages. Title of earlier version was: Some short proofs for connectedness of boundaries

Scientific paper

We generalize theorems of Kesten and Deuschel-Pisztora about the connectedness of the exterior boundary of a connected subset of $\Z^d$, where "connectedness" and "boundary" are understood with respect to various graphs on the vertices of $\Z^d$. 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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