Analysis of approximate algorithms for constrainedand unconstrained edge - coloring of bipartite

The problem of edge-coloring a bipartite graph is to color the edges so that adjacent edges receive di erent colors. An optimal algorithm uses the minimum number of colors to color the edges. We consider several approximation algorithms for edge-coloring bipartite graphs and show tight bounds on the number of colors they use in the worst case. We also brie y consider the constrained edge-coloring problem where each color may be used to color at most k edges, and obtain bounds on the number of colors used by the approximation algorithms in the worst case.