This paper gives a new and faster algorithm to find a 1-factor in a bipartite ∆-regular graph. The time complexity of this algorithm is O(n∆ + n log n log ∆), where n is the number of nodes. This implies an O(n log n log ∆ + m log ∆) algorithm to edge-color a bipartite graph with n nodes, m edges, and maximum degree ∆.
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