The List Colouring Conjecture for line graphs

Let a graph $G$ be edge $k$-colourable if its line graph is $k$-colourable, and edge $k$-choosable if its line graph is $k$-choosable. The List Colouring Conjecture. Every edge $k$-colourable graph is edge $k$-choosable. This is a longstanding conjecture about whether the chromatic and choice numbers of every line graph coincide; the supplied text gives no resolution evidence.