Zhang–Liu–Wang conjecture on the adjacent vertex distinguishing chromatic index

Let GG be a finite simple graph with no isolated vertices. Write V(G)V(G) and E(G)E(G) for its vertex and edge sets, let Δ(G)\Delta(G) be its maximum degree, and let χa(G)\chi'_{a}(G) denote the smallest number of colors in an adjacent vertex distinguishing edge coloring of GG. A graph is normal if it contains no isolated edges. Zhang–Liu–Wang's conjecture. If GG is a connected normal graph different from a 55-cycle and satisfies V(G)3|V(G)|\geqslant 3, then

χa(G)Δ(G)+2.\chi'_{a}(G)\leqslant\Delta(G)+2.

The conjecture concerns an upper bound for the adjacent vertex distinguishing chromatic index in terms of maximum degree. The supplied source does not state whether the conjecture has been resolved.

Sources & referencesView supporting material

Primary source

Lianzhu Zhang, Weifan Wang and Ko-Wei Lih, “An improved upper bound on the adjacent vertex distinguishing chromatic index of a graph”, arXiv:1208.2315 (2012).

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