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Complexity properties of complementary prisms

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Abstract

The complementary prism \(G\bar{G}\) of a graph G arises from the disjoint union of the graph G and its complement \(\bar{G}\) by adding the edges of a perfect matching joining pairs of corresponding vertices of G and \(\bar{G}\). 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 \(P_3\)-convexity. We establish hardness results and identify some efficiently solvable cases.

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Acknowledgments

The research reported here was done during a visit of Marcio Antônio Duarte and Uéverton dos Santos Souza at Ulm University.

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Authors and Affiliations

  1. Universidade Federal de Goiás, Goiânia, Brazil

    Marcio Antônio Duarte

  2. Institut für Optimierung und Operations Research, Universität Ulm, Ulm, Germany

    Lucia Penso & Dieter Rautenbach

  3. Instituto de Computação, Universidade Federal Fluminense, Niterói, Brazil

    Uéverton dos Santos Souza

Authors
  1. Marcio Antônio Duarte
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  2. Lucia Penso
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  3. Dieter Rautenbach
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  4. Uéverton dos Santos Souza
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Corresponding author

Correspondence to Dieter Rautenbach.

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Duarte, M.A., Penso, L., Rautenbach, D. et al. Complexity properties of complementary prisms. J Comb Optim 33, 365–372 (2017). https://doi.org/10.1007/s10878-015-9968-5

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  • DOI: https://doi.org/10.1007/s10878-015-9968-5

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