Bonamy et al.'s odd-degree planar edge-partition conjecture

Let $G$ be a planar graph of odd maximum degree $\Delta\ge 7$. A linear forest is a forest whose connected components are paths, and a matching is a set of pairwise vertex-disjoint edges.

Odd-degree planar edge-partition conjecture. The edges of $G$ can be partitioned into $\tfrac{\Delta-1}{2}$ linear forests and one matching.

The conjecture seeks a stronger decomposition than the general linear-arboricity bound in the odd-degree planar case. The paper proves this conclusion for odd maximum degree at least $9$, leaving the cases covered by the stated conjecture below that threshold open.