Total coloring is a variant of edge coloring where both vertices and edges are to be colored. A graph is totally $k$-choosable if for any list assignment of $k$ colors to each vertex and each edge, we can extract a proper total coloring. In this setting, a graph of maximum degree $\Delta$ needs at least $\Delta+1$ colors. In the planar case, Borodin proved in 1989 that $\Delta+2$ colors suffice when $\Delta$ is at least 9. We show that this bound also holds when $\Delta$ is $8$.

翻译：总颜色是边缘颜色的一种变体, 边脊和边缘都要加色。 如果对每个顶端和边缘分配任何以美元计色的列表, 则图表是完全可以选择的 $k$ 。 在此设置中, 最大度 $\ Delta$ 需要至少 $\ Delta+1$ 的颜色。 在 planar 案中, Borodin 在1989 年证明$\ Delta+2$ 的颜色在$\ Delta$ 至少是 9. 时足够, 我们显示, 当$\ Delta$ 为 8美元时, 约束也足够 。