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Progress on the Adjacent Vertex Distinguishing Edge Coloring Conjecture

par Joret, Gwenaël ;Lochet, William
Référence SIAM journal on discrete mathematics, 34, 4, page (2221-2238)
Publication Publié, 2020-01

Article révisé par les pairs

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Résumé :

A proper edge coloring of a graph is adjacent vertex distinguishing if no two adjacent vertices see the same set of colors. Using a clever application of the local lemma, Hatami [J. Combin. Theory Ser. B, 95 (2005), pp. 246-256] proved that every graph with maximum degree Δ and no isolated edge has an adjacent vertex distinguishing edge coloring with Δ + 300 colors, 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 [Appl. Math. Lett., 15 (2002), pp. 623-626] that Δ + 2 colors are enough for Δ ≥ 3.