On the cores of games arising from integer edge covering functions of graphs

Authors:
Boram Park;Suh-Ryung Kim;Hye Kyung Kim
Affiliations:
DIMACS, Rutgers University, Piscataway, USA 08854;Department of Mathematics Education, Seoul National University, Seoul, Korea 151-742;Department of Mathematics, Catholic University of Daegu, Daegu, Korea 712-702
Venue:
Journal of Combinatorial Optimization
Year:
2013

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Abstract

In this paper, we study cooperative games arising from integer edge covering problems on graphs. We introduce two games, a rigid k-edge covering game and its relaxed game, as generalizations of a rigid edge covering game and its relaxed game studied by Liu and Fang (2007). Then we give a characterization of the cores of both games, find relationships between them, and give necessary and sufficient conditions for the balancedness of a rigid k-edge covering game and its relaxed game.