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arXiv · 2509.15000

Measurable one-ended spanning trees

Matt Bowen·António Girão·Héctor Jardón-Sánchez·Grigory Terlov
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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.

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Matt Bowen, António Girão, Héctor Jardón-Sánchez, Grigory Terlov. 2025-09-18. Measurable one-ended spanning trees. https://arxiv.org/abs/2509.15000

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