# Stabilizing Weighted Graphs

@article{Koh2017StabilizingWG, title={Stabilizing Weighted Graphs}, author={Zhuan Khye Koh and Laura Sanit{\`a}}, journal={Math. Oper. Res.}, year={2017}, volume={45}, pages={1318-1341} }

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…

## 3 Citations

### Stabilization of Capacitated Matching Games

- MathematicsArXiv
- 2022

An edge-weighted, vertex-capacitated graph G is called stable if the value of a maximum-weight capacity-matching equals the value of a maximum-weight fractional capacity-matching. Stable graphs play…

### The Complexity of Matching Games: A Survey

- Economics, Computer ScienceArXiv
- 2022

This survey focuses on computational complexity aspects of various game-theoretical solution concepts, such as the core, nucleolus and Shapley value, when the input is restricted to some (generalized) matching game.

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