Edge-coloring sparse graphs with $\mathrm{\Delta }$ colors in quasilinear time

In this paper we show that every graph $G$ of bounded maximum average degree $\mathrm{m}\mathrm{a}\mathrm{d}(G)$ and with maximum degree $\mathrm{\Delta }$ can be edge-colored using the optimal number of $\mathrm{\Delta }$ colors in quasilinear time, whenever $\mathrm{\Delta }\ge 2\mathrm{m}\mathrm{a}\mathrm{d}(G)$. 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 [ESA 2024].