Improved equitable list arboricity conjecture for connected graphs

Let $G$ be a connected graph, and let $\Delta(G)$ denote its maximum degree. The graph is equitably $k$-list arborable if every $k$-assignment admits an arborable list coloring in which each color class has size at most $\lceil |V(G)|/k\rceil$.

Improved equitable list arboricity conjecture. Any connected graph $G$ is equitably $\lceil\Delta(G)/2\rceil$-list arborable provided $G$ is neither a cycle nor a complete graph of odd order.

This conjecture seeks to improve the bound in Zhang's equitable list arboricity conjecture. Its status is not specified in the supplied text.