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

Abhishek Dhawan

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arXiv · 2407.16585

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

Abhishek Dhawan

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Abstract

We present a simple $(1+\varepsilon)\Delta$-edge-coloring algorithm for graphs of maximum degree $\Delta = \Omega(\log n / \varepsilon)$ with running time $O\left(m\,\log^3 n/\varepsilon^3\right)$. 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.

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Abhishek Dhawan. 2024-07-23. A Simple Algorithm for Near-Vizing Edge-Coloring in Near-Linear Time. https://arxiv.org/abs/2407.16585

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