Abstract
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 language | English |
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Pages (from-to) | 52-65 |
Number of pages | 14 |
Journal | Journal of Graph Theory |
Volume | 101 |
Issue number | 1 |
DOIs | |
Publication status | Published - Sept 2022 |
Keywords
- asymmetric colouring
- distinguishing number
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Geometry and Topology