Progress on the adjacent vertex distinguishing edge colouring conjecture

04/17/2018

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by   Gwenaël Joret, et al.

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A proper edge colouring of a graph is adjacent vertex distinguishing if no two adjacent vertices see the same set of colours. Using a clever application of the Local Lemma, Hatami (2005) proved that every graph with maximum degree Δ and no isolated edge has an adjacent vertex distinguishing edge colouring with Δ + 300 colours, provided Δ is large enough. We show that this bound can be reduced to Δ + 19. This is motivated by the conjecture of Zhang, Liu, and Wang (2002) that Δ + 2 colours are enough for Δ≥ 3.