The List Equitable Total Coloring Conjecture

Let $G$ be a finite simple graph, let $T(G)$ be its total graph, and let $\chi_l(T(G))$ denote the list chromatic number of $T(G)$. A graph is equitably $k$-choosable if every list assignment with lists of size $k$ admits a proper coloring in which each color is used on at most $\lceil |V(T(G))|/k\rceil$ vertices. The List Equitable Total Coloring Conjecture. For every graph $G$, the total graph $T(G)$ is equitably $k$-choosable for every

$$k\geq\max\{\chi_l(T(G)),\Delta(G)+2\}.$$

This is the natural combination of equitable total coloring and list total coloring, and the paper introduces it as an open extension of Fu's conjecture.