One-way infinite 2-walks in planar graphs
Combinatorics
2015-08-28 v1
Abstract
We prove that every 3-connected 2-indivisible infinite planar graph has a 1-way infinite 2-walk. (A graph is 2-indivisible if deleting finitely many vertices leaves at most one infinite component, and a 2-walk is a spanning walk using every vertex at most twice.) This improves a result of Timar, which assumed local finiteness. Our proofs use Tutte subgraphs, and allow us to also provide other results when the graph is bipartite or an infinite analog of a triangulation: then the prism over the graph has a spanning 1-way infinite path.
Keywords
Cite
@article{arxiv.1508.06982,
title = {One-way infinite 2-walks in planar graphs},
author = {Daniel P. Biebighauser and M. N. Ellingham},
journal= {arXiv preprint arXiv:1508.06982},
year = {2015}
}
Comments
23 pages, 4 figures