  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.
