The 3-edge-colouring conjecture for cubic Cayley graphs

Let $G$ be a finite group and let $S\subset G$. The generalized orbital graph $\Gamma_{G/H,S}$ has node set $G/H$ and edge set generated by the pairs $\{H,gH\}$ for $g\in S$. When $H=\{\operatorname{id}\}$, it is a Cayley graph. A cubic Cayley graph is a Cayley graph in which every node has degree three, and a 3-edge colouring is a proper assignment of three colours to its edges so that the three edges incident to each node have distinct colours.

3-edge-colouring conjecture. Every cubic Cayley graph admits a 3-edge colouring.

Such a colouring would provide a way to construct cycle double covers of cubic Cayley graphs, which is relevant to the construction of vertex-transitive graphs and simplicial surfaces with prescribed automorphism groups. The supplied text does not state whether this conjecture has been resolved.