Measurable one-ended spanning trees

Published 18 Sep 2025 in math.LO, math.CO, and math.PR | (2509.15000v1)

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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