A Note on Balancedness of Dominating Set Games

Qizhi Fang () and Hye Kyung Kim ()
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Qizhi Fang: Ocean University of China
Hye Kyung Kim: Catholic University of Daegu

Journal of Combinatorial Optimization, 2005, vol. 10, issue 4, No 1, 303-310

Abstract: Abstract In this paper we consider the balancedness of dominating set games, introduced by Velzen 2003. We establish a new kind of 0-1 program formulation to model the domination problem on graphs, and give a strong connection between LP relaxation of this 0-1 program and the cost allocation problem concerning the core of a dominating set game. Duality theory on Lagrange dual is the main technique in our proof. In particular, we use this insight to give the equivalence of the balancedness for two different dominating set games.

Keywords: core; balancedness; Lagrange dual; rigid dominating set game; relaxed dominating set game (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10878-005-4920-8

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