Kostochka–Yu equitable list-coloring Ore conjecture

For a graph $G$, define its Ore-degree by

$$\Theta(G):=\max\{d(x)+d(y):xy\in E(G)\}.$$

A graph is equitably $k$-choosable if every $k$-list assignment admits a proper coloring in which each color class has size at most $\lceil|V(G)|/k\rceil$. Kostochka–Yu's conjecture. Every graph $G$ is equitably $(1+0.5\Theta(G))$-choosable. The source reports partial results for graphs with $\Theta(G)\leq6$.