Stabilizing Weighted Graphs

  title={Stabilizing Weighted Graphs},
  author={Zhuan Khye Koh and Laura Sanit{\`a}},
  journal={Math. Oper. Res.},
An edge-weighted graph [Formula: see text] is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in network bargaining games and cooperative matching games, because they characterize instances that admit stable outcomes. We give the first polynomial-time algorithm to find a minimum cardinality subset of vertices whose removal from G yields a stable graph, for any weighted graph G. The algorithm… 

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