  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 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
[ESA 2024].
