A Simple Algorithm for Near-Vizing Edge-Coloring in Near-Linear Time

Abstract

We present a simple $(1+\epsilon )\Delta$-edge-coloring algorithm for graphs of maximum degree $\Delta =\Omega (\log n/\epsilon )$ with running time $O\left(m{\log }^{3}n/{\epsilon }^3\right)$. Our algorithm improves upon that of [Duan, He, and Zhang; SODA19], which was the first near-linear time algorithm for this problem. While our results are weaker than the current state-of-the-art, our approach is significantly simpler, both in terms of analysis as well as implementation, and may be of practical interest.

arXiv comment22 pages, 6 figures