Frucht's theorem in Borel setting
Logic
2022-05-16 v1 Combinatorics
Abstract
In this paper, we show that Frucht's theorem holds in Borel setting. More specifically, we prove that any standard Borel group can be realized as the Borel automorphism group of a Borel graph. A slight modification of our construction also yields the following result in topological setting: Any Polish group can be realized as the homeomorphic automorphism group of a -graph on a Polish space.
Cite
@article{arxiv.2205.06335,
title = {Frucht's theorem in Borel setting},
author = {Onur Bilge and Burak Kaya},
journal= {arXiv preprint arXiv:2205.06335},
year = {2022}
}