Gastineau–Togni and Hocquard–Lajou–Lužar conjecture on $(1,2^7)$-edge-coloring

For a graph $G$, a $(1,2^7)$-edge-coloring partitions $E(G)$ into one matching and seven induced matchings. A graph is subcubic if its maximum degree is at most $3$.

The $(1,2^7)$-edge-coloring conjecture. Every subcubic graph is $(1,2^7)$-edge-colorable.

Gastineau and Togni first asked this as an open question for cubic graphs, while Hocquard, Lajou, and Lužar conjectured the stated subcubic version. The paper reports it as unresolved; known results establish the weaker $(1,2^8)$-edge-coloring bound.