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

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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.

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Acknowledgements

We wish to acknowledge an anonymous referees for suggestions leading to improvements in the presentation of the results.

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Authors and Affiliations

  1. DIMACS, Rutgers University, Piscataway, NJ, 08854, USA

    Boram Park

  2. Department of Mathematics Education, Seoul National University, Seoul, 151-742, Korea

    Suh-Ryung Kim

  3. Department of Mathematics, Catholic University of Daegu, Daegu, 712-702, Korea

    Hye Kyung Kim

Authors
  1. Boram Park
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  2. Suh-Ryung Kim
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  3. Hye Kyung Kim
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Corresponding author

Correspondence to Suh-Ryung Kim.

Additional information

The research of Boram Park and Hye Kyung Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) fund by the Ministry of Education, Science and Technology (No. 2010-0022665).

The research of Suh-Ryung Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0009933).

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Park, B., Kim, SR. & Kim, H.K. On the cores of games arising from integer edge covering functions of graphs. J Comb Optim 26, 786–798 (2013). https://doi.org/10.1007/s10878-012-9484-9

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  • DOI: https://doi.org/10.1007/s10878-012-9484-9

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