Core stability of vertex cover games

Authors:
Qizhi Fang;Liang Kong
Affiliations:
Department of Mathematics, Ocean University of China, Qingdao, P.R. China;Department of Mathematics, Ocean University of China, Qingdao, P.R. China
Venue:
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Year:
2007

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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.