A Stallings type theorem for quasi-transitive graphs

Matthias Hamann, Florian Lehner, Babak Miraftab, Tim Rühmann

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)40-69
Number of pages30
JournalJournal of Combinatorial Theory. Series B
Publication statusPublished - Nov 2022
Externally publishedYes


  • Infinite graphs
  • Transitivity
  • Tree-decompositions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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