Abstract
In this paper, we focus on the core stability of vertex cover games, which arise from vertex cover problems on graphs. Based on duality theory of linear programming, we first prove that a balanced vertex cover game has the stable core if and only if every edge belongs to a maximum matching in the corresponding graph. We also show that for a totally balanced vertex cover game, the core largeness, extendability and exactness are all equivalent, which imply the core stability.
This work is supported by NCET (No.05-0598) and NSFC (No.10771200).
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Fang, Q., Kong, L. (2007). Core Stability of Vertex Cover Games. In: Deng, X., Graham, F.C. (eds) Internet and Network Economics. WINE 2007. Lecture Notes in Computer Science, vol 4858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77105-0_52
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DOI: https://doi.org/10.1007/978-3-540-77105-0_52
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