Breaking small automorphisms by list colourings
Combinatorics
2023-06-22 v1
Abstract
For a graph G, we define a small automorphism as one that maps some vertex into its neighbour. We investigate the edge colourings of G that break every small automorphism of G. We show that such a colouring can be chosen from any set of lists of length three. In addition, we show that any set of lists of length two on both edges and vertices of G yields a total colouring which breaks all the small automorphisms of . These results are sharp and they match the non-list variants.
Cite
@article{arxiv.2306.12178,
title = {Breaking small automorphisms by list colourings},
author = {Jakub Kwaśny and Marcin Stawiski},
journal= {arXiv preprint arXiv:2306.12178},
year = {2023}
}