Finding 1-Factors in Bipartite Regular Graphs and Edge-Coloring Bipartite Graphs

Abstract

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