Measurable one-ended spanning trees
Logic
2025-09-22 v2 Combinatorics
Probability
Abstract
We show that a one-ended, locally finite, measurable graph on a standard probability space admits a measurable one-ended spanning subtree if and only if it is measure-hyperfinite. This answers a question posed by Bowen, Poulin, and Zomback and extends recent results of Tim\'ar and Conley, Gaboriau, Marks, and Tucker-Drob.
Keywords
Cite
@article{arxiv.2509.15000,
title = {Measurable one-ended spanning trees},
author = {Matt Bowen and António Girão and Héctor Jardón-Sánchez and Grigory Terlov},
journal= {arXiv preprint arXiv:2509.15000},
year = {2025}
}