$\Delta +300$ is a Bound on the Adjacent Vertex Distinguishing Edge Chromatic Number

Abstract

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 $\Delta$ and with no isolated edges has an \avd-coloring with at most $\Delta +300$ colors, provided that $\Delta >10^{20}$.