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arXiv · 2302.13312

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

Marthe Bonamy·Jadwiga Czyżewska·Łukasz Kowalik·Michał Pilipczuk
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Abstract

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 $Δ\ge 9$ can be partitioned into $\tfrac{Δ-1}{2}$ 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 $\lceil(Δ+1)/2\rceil$ [Wu, 1999].

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Marthe Bonamy, Jadwiga Czyżewska, Łukasz Kowalik, Michał Pilipczuk. 2023-02-26. Partitioning edges of a planar graph into linear forests and a matching. https://arxiv.org/abs/2302.13312

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