Electronic Communications in Probability

One-ended spanning trees in amenable unimodular graphs

Ádám Timár

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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.

Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 72, 12 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1573528177

Digital Object Identifier
doi:10.1214/19-ECP274

Zentralblatt MATH identifier
07142643

Subjects
Primary: 60C05: Combinatorial probability

Keywords
invariant spanning tree unimodular random graph factor of iid one-ended

Rights
Creative Commons Attribution 4.0 International License.

Citation

Timár, Ádám. One-ended spanning trees in amenable unimodular graphs. Electron. Commun. Probab. 24 (2019), paper no. 72, 12 pp. doi:10.1214/19-ECP274. https://projecteuclid.org/euclid.ecp/1573528177


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References

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