Frucht’s theorem in Borel setting

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BİLGE O., KAYA B.

Periodica Mathematica Hungarica, cilt.88, sa.1, ss.59-67, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 88 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s10998-023-00537-2
  • Dergi Adı: Periodica Mathematica Hungarica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.59-67
  • Anahtar Kelimeler: 03E15, 05C25, Borel graphs, Descriptive graph combinatorics, Frucht’s theorem
  • Gazi Üniversitesi Adresli: Evet

Özet

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.