A graph G is k-edge-choosable if every instance of list edge-coloring that has G as its underlying graph and that provides at least k allowed colors for each edge of G has a proper coloring.
The edge choosability, or list edge colorability, list edge chromatic number, or list chromatic index, ch'(G) of graph G is the least number k such that G is k-edge-choosable.
Some properties of ch'(G): Here χ′(G) is the chromatic index of G; and Kn,n, the complete bipartite graph with equal partite sets.
This conjecture has a fuzzy origin; Jensen & Toft (1995) overview its history.
The Dinitz conjecture, proven by Galvin (1995), is the special case of the list coloring conjecture for the complete bipartite graphs Kn,n.