For a bipartite multigraph, the list chromatic index is equal to the chromatic index (which is, of course, the same as the maximum degree). This generalizes Janssen′s result on complete bipartite graphs Km, n with m ≠ n; in the case of Kn, n, it answers a question of Dinitz. (The list chromatic index of a multigraph is the least number n for which the edges can be colored so that adjacent edges get different colors, the color of each edge being chosen from an arbitrarily prescribed list of n different colors associated with that edge.)
