Strong arboricity versus arboricity conjecture

Let $G$ be a graph. Write $\operatorname{arb}(G)$ for its arboricity, the least number of colors in an edge coloring with no monochromatic cycle, and write $\zeta(G)$ for its strong arboricity, the least number of colors in a coloring that remains acyclic after contracting any single edge.

Strong arboricity conjecture. Every graph $G$ satisfies

$$\zeta(G)\leqslant 2\operatorname{arb}(G).$$

For complete graphs, the paper notes that $\zeta(K_n)=2\operatorname{arb}(K_n)-1$, motivating this proposed general upper bound.