In this paper we show that every graph $G$ of bounded maximum average degree ${\rm mad}(G)$ and with maximum degree $\Delta$ can be edge-colored using the optimal number of $\Delta$ colors in quasilinear expected time, whenever $\Delta\ge 2{\rm mad}(G)$. The maximum average degree is within a multiplicative constant of other popular graph sparsity parameters like arboricity, degeneracy or maximum density. Our algorithm extends previous results of Chrobak and Nishizeki [J. Algorithms, 1990] and Bhattacharya, Costa, Panski and Solomon [arXiv, 2023].

翻译：本文证明：对于任意具有有界最大平均度${\rm mad}(G)$且最大度为$\Delta$的图$G$，当$\Delta\ge 2{\rm mad}(G)$时，可以在拟线性期望时间内使用$\Delta$种最优颜色对其进行边着色。最大平均度与树状度、退化度或最大密度等其他常用图稀疏性参数仅相差一个乘法常数。我们的算法改进了Chrobak和Nishizeki [J. Algorithms, 1990] 以及Bhattacharya、Costa、Panski和Solomon [arXiv, 2023] 的先前结果。