Cyclic coloring conjecture for subdivisions of simple 3-connected plane graphs

Let $G$ be a subdivision of a simple $3$-connected plane graph. Define $t(G)$ to be the maximum number of subdivision vertices on an edge of the underlying graph, and let $\Delta^*(G)$ be the maximum face degree. Write $\chi_c(G)$ for the minimum number of colors in a cyclic coloring, meaning a vertex coloring in which vertices incident with the same face receive distinct colors.

Subdivision cyclic coloring conjecture. Every such graph $G$ satisfies

$$\chi_c(G) \leq \Delta^*(G)+t(G)+2.$$

The source introduces this as a new conjecture combining the Plummer–Toft conjecture with the corresponding subdivision case of the earlier conjecture. Its status is not resolved in the supplied text.