Measurable one-ended spanning trees
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914046828085248 |
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| author | Bowen, Matt Girão, António Jardón-Sánchez, Héctor Terlov, Grigory |
| author_facet | Bowen, Matt Girão, António Jardón-Sánchez, Héctor Terlov, Grigory |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measurable one-ended spanning trees Bowen, Matt Girão, António Jardón-Sánchez, Héctor Terlov, Grigory Logic Combinatorics Probability 03E15, 05C25, 05C63, 37A20, 60K35 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. |
| title | Measurable one-ended spanning trees |
| topic | Logic Combinatorics Probability 03E15, 05C25, 05C63, 37A20, 60K35 |
| url | https://arxiv.org/abs/2509.15000 |