Bulletin of the
Korean Mathematical Society BKMS

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.

Keywords: dominating function, fractional dominating number, fractional domination game, core, concavity

MSC numbers: 91A12, 68R01