• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.265-275
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• 2006

In this paper, we introduce a fractional domination game arising from fractional domination problems on graphs and focus on its balancedness and concavity. We first characterize the core of the fractional domination game and show that its core is always non-empty taking use of dual theory of linear programming. Furthermore we study concavity of this game.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.49-55
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• 2009

A cooperative game often arises from domination problem on graphs and the core in a cooperative game could be the optimal solution of a linear programming of a given game. In this paper, we define a {k}-fractional domination game which is a specific type of fractional domination games and find the core of a {k}-fractional domination game. Moreover, we may investigate the balancedness of a {k}-fractional domination game using a concept of a linear programming and duality. We also conjecture the concavity for {k}-fractional dominations game which is important problem to find the elements of the core.