Edwards et al.'s distance-2 matching edge-coloring conjecture

Let $G$ be a graph with maximum degree $\Delta$, and let $H$ be a subgraph of $G$. A matching $H$ is distance-2 when the distance in $G$ between any two vertices in distinct components of $H$ is at least $2$. An $(\Delta+1)$-edge-coloring of $H$ is a proper edge-coloring using $\Delta+1$ colors.

Edwards et al.'s conjecture. If $H$ is a distance-2 matching, then every $(\Delta+1)$-edge-coloring of $H$ extends to a $(\Delta+1)$-edge-coloring of $G$.

The conjecture is the edge-coloring analogue motivating the paper's total-coloring extension conjectures. Its resolution status is not specified in the supplied text.