Local finiteness, distinguishing numbers and Tucker's conjecture
Combinatorics
2015-04-30 v2
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.
Keywords
Cite
@article{arxiv.1412.0881,
title = {Local finiteness, distinguishing numbers and Tucker's conjecture},
author = {Florian Lehner and Rögnvaldur G. Möller},
journal= {arXiv preprint arXiv:1412.0881},
year = {2015}
}