In matching theory, n-critical graphs play an important role in the decomposition of graphs with respect to perfect matchings. Since bipartite graphs cannot be n-critical when n > 0, we amend the classical definition of n-critical graphs and propose the concept of n-critical bipartite graphs. Let G = (B, W; E) be a bipartite graph with n = |W| - |B|, where B and W are the bipartitions of vertex set, E is the edge set. Then, G is n-critical if when deleting any n distinct vertices of W, the remaining subgraph of G has a perfect matching. Furthermore, an algorithm for determining n-critical bipartite graphs is given which runs in O(|W||E|) time, in the worst case. Our work helps to design a job assignment circuit which has high robustness.
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机译：在匹配理论中，N-Critic图表在关于完美匹配的图表分解中起重要作用。由于双方图表在n> 0时不能n-truess，因此我们修改了N-Critical图的经典定义，并提出了n-Critical二分图的概念。设g =（b，w; e）是n = | w的二分图| w | - | B |，其中B和W是顶点集的两分，E是边框。然后，如果在删除W的任何N个不同顶点时，G是关键的，则G的剩余子图具有完美的匹配。此外，给出了一种确定N-关键二分体图的算法，其在最坏的情况下在O（| W || e |）时间内运行。我们的作品有助于设计具有高稳健性的工作分配电路。
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