A Stallings type theorem for quasi-transitive graphs

Matthias Hamann, Florian Lehner, Babak Miraftab, Tim Rühmann

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung


We consider locally finite, connected, quasi-transitive graphs and show that every such graph with more than one end is a tree amalgamation of two other such graphs. This can be seen as a graph-theoretical version of Stallings' splitting theorem for multi-ended finitely generated groups and indeed it implies this theorem. Our result also leads to a characterisation of accessible graphs. We obtain applications of our results for planar graphs (answering a variant of a question by Mohar in the affirmative) and graphs without thick ends.

Seiten (von - bis)40-69
FachzeitschriftJournal of Combinatorial Theory. Series B
PublikationsstatusVeröffentlicht - Nov. 2022
Extern publiziertJa

ASJC Scopus subject areas

  • Theoretische Informatik
  • Diskrete Mathematik und Kombinatorik
  • Theoretische Informatik und Mathematik


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