Edge-critical graphs and list colorings

A graph G is said to be Δ-edge-critical if it is not Δ-edge-colorable but every edge-deleted subgraph is Δ-edge-colorable. (Here and in the sequel Δ is the maximum degree of G.)

At the time of the 18th British Combinatorial Conference (July 2001) I made the following

Conjecture: Suppose that G is a Δ-edge-critical graph. Suppose that for each edge e of G, there is a list L(e) of Δ colors. Then G is L-edge-colorable if and only if all lists are equal to each other.

Send comments to Bojan.Mohar@uni-lj.si

Revised: julij 26, 2001.