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2019 One-ended spanning trees in amenable unimodular graphs
Ádám Timár
Electron. Commun. Probab. 24: 1-12 (2019). DOI: 10.1214/19-ECP274

Abstract

We prove that every amenable one-ended Cayley graph has an invariant one-ended spanning tree. More generally, for any one-ended amenable unimodular random graph we construct a factor of iid percolation (jointly unimodular subgraph) that is almost surely a one-ended spanning tree. In [2] and [1] similar claims were proved, but the resulting spanning tree had 1 or 2 ends, and one had no control of which of these two options would be the case.

Citation

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Ádám Timár. "One-ended spanning trees in amenable unimodular graphs." Electron. Commun. Probab. 24 1 - 12, 2019. https://doi.org/10.1214/19-ECP274

Information

Received: 13 June 2018; Accepted: 31 October 2019; Published: 2019
First available in Project Euclid: 12 November 2019

zbMATH: 07142643
MathSciNet: MR4040939
Digital Object Identifier: 10.1214/19-ECP274

Subjects:
Primary: 60C05

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