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

Author

Listed:
  • Boram Park

    (Rutgers University)

  • Suh-Ryung Kim

    (Seoul National University)

  • Hye Kyung Kim

    (Catholic University of Daegu)

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.

Suggested Citation

  • Boram Park & Suh-Ryung Kim & Hye Kyung Kim, 2013. "On the cores of games arising from integer edge covering functions of graphs," Journal of Combinatorial Optimization, Springer, vol. 26(4), pages 786-798, November.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:4:d:10.1007_s10878-012-9484-9
    DOI: 10.1007/s10878-012-9484-9
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    References listed on IDEAS

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    1. Xiaotie Deng & Toshihide Ibaraki & Hiroshi Nagamochi, 1999. "Algorithmic Aspects of the Core of Combinatorial Optimization Games," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 751-766, August.
    2. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    3. Thomas Bietenhader & Yoshio Okamoto, 2006. "Core Stability of Minimum Coloring Games," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 418-431, May.
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    Cited by:

    1. Tianhang Lu & Han Xian & Qizhi Fang, 2023. "Approximate Core Allocations for Edge Cover Games," Papers 2308.11222, arXiv.org.

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