Before revision:  We prove that the k-List Coloring, List k-Coloring, and k-Precoloring Extension problems are NP-complete on bipartite graphs with diameter at most d, for every k 4 and every d 3, and for k=3 and d 4, and that List k-Coloring is polynomial when d=2 (i.e., on complete bipartite graphs)
After revision:  We prove that the k-List Coloring, List k-Coloring, and k-Precoloring Extension problems are NP-complete on bipartite graphs with diameter at most d,  4 and every d 3, and for k=3 and d 4, and that List k-Coloring is polynomial when d=2 (i.e., on complete bipartite graphs)