We show that the edges of any planar graph of maximum degree at most $9$ can be partitioned into $4$ linear forests and a matching. Combined with known results, this implies that the edges of any planar graph $G$ of odd maximum degree $\Delta\ge 9$ can be partitioned into $\tfrac{\Delta-1}{2}$ linear forests and one matching. This strengthens well-known results stating that graphs in this class have chromatic index $\Delta$ [Vizing, 1965] and linear arboricity at most $\lceil(\Delta+1)/2\rceil$ [Wu, 1999].

翻译：我们证明：任意最大度至多为$9$的平面图，其边可分割为$4$个线性森林与一个匹配。结合已知结果，这意味着任意最大度为奇数且$\Delta\ge 9$的平面图$G$，其边可分割为$\tfrac{\Delta-1}{2}$个线性森林与一个匹配。该结论强化了已有经典结果：此类图的染色指数为$\Delta$ [Vizing, 1965]，且线性树性度至多为$\lceil(\Delta+1)/2\rceil$ [Wu, 1999]。