Hocquard–Lajou–Luar conjecture for subcubic planar graphs

For a sequence $S=(s_1,\dots,s_k)$ of non-decreasing positive integers, an $S$-packing edge-coloring of a graph $G$ is a partition of $E(G)$ into $E_1,\dots,E_k$ such that the distance between any two distinct edges in $E_i$ is at least $s_i+1$. In particular, a $(1,2^6)$-coloring has one matching and six induced matchings, while a $(1^2,2^3)$-coloring has two matchings and three induced matchings. Hocquard–Lajou–Luar's conjecture. Every subcubic planar graph is $(1,2^6)$-packing edge-colorable and $(1^2,2^3)$-packing edge-colorable. These bounds concern intermediate edge-colorings between proper and strong edge-colorings. The conjecture is open in the supplied source context.