We say that an edge colouring breaks an automorphism if some edge is mapped to an edge of a different colour. We say that the colouring is distinguishing if it breaks every non-identity automorphism. We show that such a colouring can be chosen from any set of lists associated to the edges of a graph G, whenever the size of each list is at least Δ − 1, where Δ is the maximum degree of G, apart from a few exceptions. This holds both for finite and infinite graphs. The bound is optimal for every Δ ≥ 3, and it is the same as in the non-list version.
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Jakub Kwaśny
Marcin Stawiski
Ars Mathematica Contemporanea
Jagiellonian University
AGH University of Krakow
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Kwaśny et al. (Tue,) studied this question.
www.synapsesocial.com/papers/69c4cddcfdc3bde44891aa77 — DOI: https://doi.org/10.26493/1855-3974.3536.fc8
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