Abstract. Given a graph [Formula: see text] and an integer [Formula: see text], let [Formula: see text] denote the minimum number of colors required to color the edges of [Formula: see text] such that, in each color class, the subgraph induced by the edges of that color has all nonzero degrees congruent to 1 modulo [Formula: see text]. In 1992, Pyber proved that [Formula: see text] for every graph [Formula: see text], and posed the question of whether [Formula: see text] can be bounded solely in terms of [Formula: see text] for every [Formula: see text]. This question was answered in 1997 by Scott, who showed that [Formula: see text], and further asked whether [Formula: see text]. Recently, Botler, Colucci, and Kohayakawa (2023) answered Scott’s question affirmatively proving that [Formula: see text], and conjectured that the multiplicative constant could be reduced to 1. A step towards this latter conjecture was made in 2024 by Nweit and Yang, who improved the bound to [Formula: see text]. In this paper, we further improve the multiplicative constant to 9. More specifically, we prove that there is a function [Formula: see text] for which [Formula: see text] if [Formula: see text] is odd, and [Formula: see text] if [Formula: see text] is even. In doing so, we prove that [Formula: see text] for every [Formula: see text]-degenerate graph [Formula: see text], which plays a central role in our proof.