The most famous open problem about list edge-coloring is probably the list coloring conjecture.
- ch′(G) = χ′(G).
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.
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