Normal 6-edge-coloring conjecture for bridgeless cubic graphs

Let $G$ be a bridgeless cubic graph, and let $\chi'_N(G)$ denote the least number of colors in a normal edge-coloring of $G$, where every edge is poor or rich. Normal 6-edge-coloring conjecture. Every bridgeless cubic graph $G$ satisfies

$$\chi'_N(G)\leq 6.$$

A normal 6-edge-coloring would improve the general normal 7-edge-coloring theorem and is established in the paper for several classes, including claw-free bridgeless cubic graphs, permutation snarks, and tree-like snarks. The conjecture remains open in general.