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：我们显示,最多9美元的顶部平面图的边缘可以分割成4美元线性森林和匹配。结合已知结果,这意味着,任何单面图的边缘可以分割成1美元/Delta\ge 9美元/G$(奇数最大度为$/Delta+$/%1>2}美元/线性森林和一个匹配。这加强了众所周知的结果,显示该类图的色度指数为$/Delta$(Visiling,1965年)和线性厌性,最多为$\lceil(\Delta+1>/2\rcele$(Wu,1999年)。</s>