Using euler partitions to edge color bipartite multigraphs

An algorithm for finding a minimal edge coloring of a bipartite multigraph is presented. The algorithm usesO(V1/2ElogV + V) time andO(E + V) space. It is based on a divide-and-conquer strategy, using euler partitions to divide the graph. A modification of the algorithm for matching is described. This algorithm finds a maximum matching of a regular bipartite graph with all degrees 2n, inO(E + V) time andO(E + V) space.