The $(\Delta(G)+2)$-edge-coloring equivalence conjecture

Let $G$ be a graph with maximum degree $\Delta(G)$, and let an edge-coloring be proper when adjacent edges receive different colors. Two edge-colorings are equivalent if one can be transformed into the other by a sequence of Kempe swaps.

The $(\Delta(G)+2)$-edge-coloring equivalence conjecture. All $(\Delta(G)+2)$-edge-colorings of a graph $G$ are equivalent.

The claim concerns connectivity of the reconfiguration space of edge-colorings under Kempe swaps. The supplied source gives no resolution status.