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

Details $Δ+300$ is a Bound on the Adjacent Vertex Distinguishing Edge Chromatic Number $Δ+300$ is a Bound on the Adjacent Vertex Distinguishing Edge Chromatic Number

2006-12-31

arxiv.org/abs/math/0701012v1

J. Combin. Theory Ser. B 95(2) (2005) pp. 246-256

Mathematics

Combinatorics

Scientific paper

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 $\Delta >10^{20}$.

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