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For a graph G and an integer k 2, a '₊-coloring of G is an edge coloring of G such that the subgraph induced by the edges of each color has all degrees congruent to 1 ~ (k), and '₊ (G) is the minimum number of colors in a '₊-coloring of G. In "The mod k chromatic index of graphs is O (k) ", J. Graph Theory. 2023; 102: 197-200, Botler, Colucci and Kohayakawa proved that '₊ (G) 198k-101 for every graph G. In this paper, we show that '₊ (G) 177k-93.
Nweit et al. (Wed,) studied this question.
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