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Inheritance of convexity for the $\mathcal {P}_{\min }$-restricted game

Abstract : We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the sub-components corresponding to a minimum partition. This minimum partition Pmin is induced by the deletion of the minimum weight edges. We provide a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with Pmin. Moreover, we prove that these graphs can be recognized in polynomial time.
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https://halshs.archives-ouvertes.fr/halshs-02960813
Contributor : Alexandre Skoda <>
Submitted on : Thursday, October 8, 2020 - 12:04:25 AM
Last modification on : Tuesday, January 19, 2021 - 11:08:38 AM

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Alexandre Skoda. Inheritance of convexity for the $\mathcal {P}_{\min }$-restricted game. Mathematical Methods of Operations Research, Springer Verlag, 2020, ⟨10.1007/s00186-020-00728-4⟩. ⟨halshs-02960813⟩

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