Achieve near-optimal palette size for deterministic list edge coloring

Achieve the same \widetilde O(\log^2 n) deterministic round complexity for list edge coloring using (1+\varepsilon)\Delta colors, for every fixed \varepsilon>0 and throughout the range \Delta\geq\Delta_0(\varepsilon).

Background

The paper gives a deterministic \widetilde O(\log^2 n)-round algorithm for list (\frac32+\varepsilon)\Delta-edge coloring when \Delta is sufficiently large as a function of \varepsilon, improving the complexity of derandomized approaches in the small-degree regime. The authors identify reducing the palette from (\frac32+\varepsilon)\Delta to (1+\varepsilon)\Delta while preserving the same round complexity as an unresolved problem.