2023-08-09
Factor-of-iid balanced orientation of non-amenable graphs
Publication
Publication
European Journal of Combinatorics , Volume 115 p. 103784:1- 103784:20
We show that if a non-amenable, quasi-transitive, unimodular graph G has all degrees even then it has a factor-of-iid balanced orientation, meaning each vertex has equal in- and outdegree. This result involves extending earlier spectral-theoretic results on Bernoulli shifts to the Bernoulli graphings of quasi-transitive, unimodular graphs. As a consequence, we also obtain that when G is regular (of either odd or even degree) and bipartite, it has a factor-of-iid perfect matching. This generalizes a result of Lyons and Nazarov beyond transitive graphs.
Additional Metadata | |
---|---|
doi.org/10.1016/j.ejc.2023.103784 | |
European Journal of Combinatorics | |
Bencs, F., Hrušková, A., & Tóth, L. M. (2023). Factor-of-iid balanced orientation of non-amenable graphs. European Journal of Combinatorics, 115, 103784:1–103784:20. doi:10.1016/j.ejc.2023.103784 |