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

Hamed Hatami

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

Combinatorics 2007-05-23 v1

Authors: Hamed Hatami

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 $\Delta >10^{20}$ .

Keywords

adjacent vertex distinguishing edge-coloring avd-coloring maximum degree graph coloring bound

Cite

@article{arxiv.math/0701012,
  title  = {$\Delta+300$ is a Bound on the Adjacent Vertex Distinguishing Edge Chromatic Number},
  author = {Hamed Hatami},
  journal= {arXiv preprint arXiv:math/0701012},
  year   = {2007}
}

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