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An edge coloring of a graph G is a process of assigning colors to the adjacent edges so that the adjacent edgesrepresents the different colors. In this paper, an algorithm isproposed to find the perfect color matching of the regularbipartite multigraph with low time complexity. For that, theproposed algorithm is divided into two procedures. In the firstprocedure, the possible circuits and bad edges are extracted fromthe regular bipartite graph. In the second procedure, the badedges are rearranged to obtain the perfect color matching. Thedepth first search (DFS) algorithm is used in this paper fortraversing the bipartite vertices to find the closed path, openpath, incomplete components, and bad edges. By the proposedalgorithm, the proper edge coloring of D – regular bipartitemulti-graph can be obtained in O (D.V) time.

A Low Complexity based Edge Color Matching Algorithm for Regular Bipartite Multigraph