English

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 Zd\mathbb{Z}^d, where "connectedness" and "boundary" are understood with respect to various graphs on the vertices of Zd\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.

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

R2 v1 2026-06-21T09:42:24.659Z