Abstract
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 K m, n with m ≠ n; in the case of K n, 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.)
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