Frucht’s theorem in Borel setting

Creative Commons License

BİLGE O., KAYA B.

Periodica Mathematica Hungarica, vol.88, no.1, pp.59-67, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 88 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1007/s10998-023-00537-2
  • Journal Name: Periodica Mathematica Hungarica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.59-67
  • Keywords: 03E15, 05C25, Borel graphs, Descriptive graph combinatorics, Frucht’s theorem
  • Gazi University Affiliated: Yes

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 Σ20 -graph on a Polish space.