Borodin–Kostochka–Woodall's List Total Coloring Conjecture

Let $G$ be a finite multigraph, and let $T(G)$ be its total graph. Write $\chi(T(G))$ for the chromatic number and $\chi_l(T(G))$ for the list chromatic number. Borodin–Kostochka–Woodall's conjecture.

$$\chi(T(G))=\chi_l(T(G)).$$

Thus total graphs should be chromatic-choosable. The conjecture has been verified for certain planar graphs and multicircuits, but the paper does not report a general resolution.