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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.
Kwaśny et al. (Mon,) studied this question.