Analysis of Approximate Algorithms for Constrained and Unconstrained Edge-coloring of Bipartite Graphs Applied Research Bellcore

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