is a bound on the adjacent vertex distinguishing edge chromatic number

An adjacent vertex distinguishing edge-coloring or an avd-coloring of a simple graph G is a proper edge-coloring of G such that no pair of adjacent vertices meets the same set of colors. We prove that every graph with maximum degree Δ and with no isolated edges has an avd-coloring with at most Δ + 300 colors, provided that Δ > 10 20 .