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A Simple Algorithm for Near-Vizing Edge-Coloring in Near-Linear Time (2407.16585v1)

Published 23 Jul 2024 in cs.DS and math.CO

Abstract: We present a simple $(1+\varepsilon)\Delta$-edge-coloring algorithm for graphs of maximum degree $\Delta = \Omega(\log n / \varepsilon)$ with running time $O\left(m\,\log3 n/\varepsilon3\right)$. 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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