An Algorithm for Determining Critical Bipartite Graphs

A matching which saturates all the vertices of a graph is called a perfect matching. Let G_B=(U, W) be a bipartite graph with bipartitions U and W, where |U| = |W|-1 and |U|>;=1. Bipartite graph G_B is called critical bipartite graph if the following property holds: graph G_B has a perfect matching after removing any vertex of W. Critical bipartite graph plays an important role in the design of robust job assignment circuit. This paper proposes one sufficient and necessary condition of critical bipartite graph. Based on this result, a determining algorithm is developed which is superior to the best algorithm known by far. The time complexity of our algorithm is linear.