On orientations preserving edge-connectivity in infinite graphs
Combinatorics
2025-10-09 v1 General Topology
Abstract
We prove that every 2k-edge-connected graph with countably many edge-ends admits a k-arc-connected orientation, extending the previous result by Assem, Koloschin and Pitz that also assumed the hypothesis of the graph being locally finite. We prove that, if every locally finite graph has a well-balanced orientation, so does every graph. Lastly, we explore an alternative to the Nash-Williams Orientation Conjecture via topological paths, and prove that it is true for every finitely separated graph.
Cite
@article{arxiv.2510.06449,
title = {On orientations preserving edge-connectivity in infinite graphs},
author = {Leandro Aurichi and Paulo Magalhães Júnior and Guilherme Eduardo Pinto},
journal= {arXiv preprint arXiv:2510.06449},
year = {2025}
}
Comments
18 pages and 9 figures