On the Bipartite Unique Perfect Matching Problem

@inproceedings{Hoang2006OnTB,
  title={On the Bipartite Unique Perfect Matching Problem},
  author={Thanh Minh Hoang and Meena Mahajan and Thomas Thierauf},
  booktitle={ICALP},
  year={2006}
}
In this note, we give tighter bounds on the complexity of the bipartite unique perfect matching problem, bipartite-UPM. We show that the problem is in C=L and in NL , both subclasses of NC. We also consider the (unary) weighted version of the problem. We show that testing uniqueness of the minimum-weight perfect matching problem for bipartite graphs is in L= and in NL. Furthermore, we show that bipartite-UPM is hard for NL. 

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