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A complete solution to the biased Alon-Krivelevich-Spencer-Szabó criterion problem for the discrepancy game Scaffolds for Higher Tropical Grassmannians: Foundations Krahn-Szegő type inequalities for graphs $\boldsymbol{2}$-Neighbor Bootstrap Percolation on Odd Graphs Modular inequalities and Alexander polynomials of pencil type conic-line arrangements Counterexamples regarding elementary symmetric partitions Bounds on Multiple $b$-Burst Deletion-Correcting Codes The mex statistic on combinatorial structures Proper Additive Edge Colorings of Regular Graphs Off-diagonal Ramsey numbers Semi-inducibility of 4-vertex graphs Combinatorial proofs of Petrie Pieri rule and Plethystic Pieri rule On Ternary Trees and Fighting Fish Asymptotic structure. III. Excluding a fat tree Asymptotic structure. V. 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Measurable one-ended spanning trees
Matt Bowen, António Girão, Héctor Jardón-Sánchez, Grigory Terlov · 2025-09-18 · via math.CO updates on arXiv.org

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 Timár and Conley, Gaboriau, Marks, and Tucker-Drob.

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