Papers › Partitioning edges of a planar graph into linear forests and a matching
Partitioning edges of a planar graph into linear forests and a matching
Marthe Bonamy, Jadwiga Czyżewska, Łukasz Kowalik, Michał Pilipczuk
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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 Δ≥9 can be partitioned into Δ-12 linear forests and one matching. This strengthens well-known results stating that graphs in this class have chromatic index Δ [Vizing, 1965] and linear arboricity at most ⌈(Δ+1)/2⌉ [Wu, 1999].
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