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Complexity properties of complementary prisms

Author

Listed:
  • Marcio Antônio Duarte

    (Universidade Federal de Goiás)

  • Lucia Penso

    (Universität Ulm)

  • Dieter Rautenbach

    (Universität Ulm)

  • Uéverton Santos Souza

    (Universidade Federal Fluminense)

Abstract

The complementary prism $$G\bar{G}$$ G G ¯ of a graph G arises from the disjoint union of the graph G and its complement $$\bar{G}$$ G ¯ by adding the edges of a perfect matching joining pairs of corresponding vertices of G and $$\bar{G}$$ G ¯ . Haynes, Henning, Slater, and van der Merwe introduced the complementary prism and as a variation of the well-known prism. We study algorithmic/complexity properties of complementary prisms with respect to cliques, independent sets, k-domination, and especially $$P_3$$ P 3 -convexity. We establish hardness results and identify some efficiently solvable cases.

Suggested Citation

  • Marcio Antônio Duarte & Lucia Penso & Dieter Rautenbach & Uéverton Santos Souza, 2017. "Complexity properties of complementary prisms," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 365-372, February.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:2:d:10.1007_s10878-015-9968-5
    DOI: 10.1007/s10878-015-9968-5
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    References listed on IDEAS

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    1. Teresa W. Haynes & Michael A. Henning & Lucas C. Merwe, 2009. "Domination and total domination in complementary prisms," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 23-37, July.
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    Cited by:

    1. João Vinicius C. Thompson & Loana T. Nogueira & Fábio Protti & Raquel S. F. Bravo & Mitre C. Dourado & Uéverton S. Souza, 2022. "A general framework for path convexities," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 994-1009, July.
    2. João Vinicius C. Thompson & Loana T. Nogueira & Fábio Protti & Raquel S. F. Bravo & Mitre C. Dourado & Uéverton S. Souza, 0. "A general framework for path convexities," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-16.

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