Bondary-connectivity via graph theory
Probability
2020-05-11 v2 Combinatorics
Abstract
We generalize theorems of Kesten and Deuschel-Pisztora about the connectedness of the exterior boundary of a connected subset of , where "connectedness" and "boundary" are understood with respect to various graphs on the vertices of . 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.
Keywords
Cite
@article{arxiv.0711.1713,
title = {Bondary-connectivity via graph theory},
author = {Adam Timar},
journal= {arXiv preprint arXiv:0711.1713},
year = {2020}
}
Comments
8 pages. Title of earlier version was: Some short proofs for connectedness of boundaries