Distinguishing infinite graphs with bounded degrees

Florian Lehner, Monika Pilsniak*, Marcin Stawiski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Call a colouring of a graph distinguishing if the only colour preserving automorphism is the identity. A conjecture of Tucker states that if every automorphism of a connected graph (Formula presented.) moves infinitely many vertices, then there is a distinguishing 2-colouring. We confirm this conjecture for graphs with maximum degree (Formula presented.). Furthermore, using similar techniques we show that if an infinite graph has maximum degree (Formula presented.), then it admits a distinguishing colouring with (Formula presented.) colours. This bound is sharp.

Original languageEnglish
Pages (from-to)52-65
Number of pages14
JournalJournal of Graph Theory
Issue number1
Publication statusPublished - Sept 2022


  • asymmetric colouring
  • distinguishing number

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Geometry and Topology


Dive into the research topics of 'Distinguishing infinite graphs with bounded degrees'. Together they form a unique fingerprint.

Cite this