Research Article

Frontiers of Mathematics in China

, Volume 5, Issue 1, pp 47-63

First online:

Algorithms for core stability, core largeness, exactness, and extendability of flow games

  • Qizhi FangAffiliated withDepartment of Mathematics, Ocean University of China Email author 
  • , Rudolf FleischerAffiliated withDepartment of Computer Science and Engineering, Fudan University
  • , Jian LiAffiliated withDepartment of Computer Science, University of Maryland
  • , Xiaoxun SunAffiliated withDepartment of Mathematics and Computing, University of Southern Queensland

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We study core stability and some related properties of flow games defined on simple networks (all edge capacities are equal) from an algorithmic point of view. We first present a sufficient and necessary condition that can be tested efficiently for a simple flow game to have a stable core. We also prove the equivalence of the properties of core largeness, extendability, and exactness of simple flow games and provide an equivalent graph theoretic characterization which allows us to decide these properties in polynomial time.


Flow network series-parallel graph imputation cooperative game


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