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http://dx.doi.org/10.4134/JKMS.2006.43.2.297

BALANCEDNESS OF INTEGER DOMINATION GAMES  

Kim, Hye-Kyung (Department of Mathematics Catholic University)
Fang Qizhi (Department of Mathematics Ocean University)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.2, 2006 , pp. 297-309 More about this Journal
Abstract
In this paper, we consider cooperative games arising from integer domination problem on graphs. We introduce two games, ${\kappa}-domination$ game and its monotonic relaxed game, and focus on their cores. We first give characterizations of the cores and the relationship between them. Furthermore, a common necessary and sufficient condition for the balancedness of both games is obtained by making use of the technique of linear programming and its duality.
Keywords
${\kappa}-domination$ function; ${\kappa}-domination$ game; monotonic ${\kappa}-domination$ game; core; balancedness;
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