Local finiteness, distinguishing numbers, and Tucker’s conjecture

Florian Lehner, Rögnvaldur G. Möller

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

A distinguishing colouring of a graph is a colouring of the vertex set such that no non-trivial automorphism preserves the colouring. Tucker conjectured that if every non-trivial automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing 2-colouring. We show that the requirement of local finiteness is necessary by giving a non-locally finite graph for which no finite number of colours suffices.

Original languageEnglish
Article numberP4.19
JournalElectronic Journal of Combinatorics
Volume22
Issue number4
DOIs
Publication statusPublished - 30 Oct 2015

Bibliographical note

Publisher Copyright:
© 2015 Australian National University. All rights reserved.

Other keywords

  • Distinguishing number
  • Infinite Graphs

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