The strong chromatic index of a multigraph is the minimum k such that the edge set can be k-colored requiring that each color class induces a matching. We verify a conjecture of Faudree, Gyárfás, Schelp and Tuza, showing that every planar multigraph with maximum degree at most 3 has strong chromatic index at most 9, which is sharp.
Kostochka, A. V., Li, X., Ruksasakchai, W., Santana, M., Wang, T., & Yu, G. (2016). Strong chromatic index of subcubic planar multigraphs. European Journal of Combinatorics, 51, 380–397. https://doi.org/10.1016/j.ejc.2015.07.002