Year: 2024
Type: article
Abstract: For a graph , we define a small automorphism as one that maps some vertex into its neighbour. We investigate the edge colourings of that break every small automorphism of . We show that such a colouring can be chosen from any set of lists of length 3. In addition, we show that any set of lists of length 2 on both edges and vertices of yields a total colouring which breaks all the small automorphisms of . These results are sharp, and they match the known bounds for the nonlist variant.
Source: Journal of Graph Theory
DOI: 10.1002/jgt.23181
Authors: Jakub Kwaśny, Marcin Stawiski
Institution: AGH University of Krakow
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402575785