Partitioning edges of a planar graph into linear forests and a matching

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 ∆ ≥ 9 can be partitioned into (∆−1)/2 linear forests and one matching. This strengthens well-known results stating that graphs in this class have chromatic index ∆ [Vizing, 1965] and linear arboricity at most ⌈(Δ+1)/2⌉.