The problem of edge-coloring a bipartite graph is to color the edges s
o that adjacent edges receive different colors. An optimal algorithm u
ses the minimum number of colors to color the edges. We consider sever
al approximation algorithms for edge-coloring bipartite graphs and sho
w tight bounds on the number of colors they use in the worst case. We
also present results on the constrained edge-coloring problem where ea
ch color may be used to color at most k edges.