Electronic Communications in Probability

One-ended spanning trees in amenable unimodular graphs

Ádám Timár

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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

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

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

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability

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

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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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