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On the $$p$$ -reinforcement and the complexity

Author

Listed:
  • You Lu

    (Northwestern Polytechnical University)

  • Fu-Tao Hu

    (University of Science and Technology of China)

  • Jun-Ming Xu

    (University of Science and Technology of China)

Abstract

Let $$G=(V,E)$$ be a graph and $$p$$ be a positive integer. A subset $$S\subseteq V$$ is called a $$p$$ -dominating set if each vertex not in $$S$$ has at least $$p$$ neighbors in $$S$$ . The $$p$$ -domination number $$\gamma _p(G)$$ is the size of a smallest $$p$$ -dominating set of $$G$$ . The $$p$$ -reinforcement number $$r_p(G)$$ is the smallest number of edges whose addition to $$G$$ results in a graph $$G^{\prime }$$ with $$\gamma _p(G^{\prime })

Suggested Citation

  • You Lu & Fu-Tao Hu & Jun-Ming Xu, 2015. "On the $$p$$ -reinforcement and the complexity," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 389-405, February.
  • Handle: RePEc:spr:jcomop:v:29:y:2015:i:2:d:10.1007_s10878-013-9597-9
    DOI: 10.1007/s10878-013-9597-9
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    References listed on IDEAS

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    1. Y. Caro & Y. Roditty, 1990. "A note on the k -domination number of a graph," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 13, pages 1-2, January.
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