Counterexamples to two conjectures on modular edge colorings of graphs

Chunqiang Guo, Baoyindureng Wu

For an integer $k\ge 2$, let ${\chi }_k^{\prime }(G)$ denote the minimum number of colors in an edge-coloring of a graph $G$ such that every nonzero degree in each color subgraph is congruent to…