Journal of Combinatorial Optimization

, Volume 33, Issue 2, pp 365–372 | Cite as

Complexity properties of complementary prisms

  • Marcio Antônio Duarte
  • Lucia Penso
  • Dieter Rautenbach
  • Uéverton dos Santos Souza


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.


Complementary prism Clique Independent set k-Domination \(P_3\)-Convexity 



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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Marcio Antônio Duarte
    • 1
  • Lucia Penso
    • 2
  • Dieter Rautenbach
    • 2
  • Uéverton dos Santos Souza
    • 3
  1. 1.Universidade Federal de GoiásGoiâniaBrazil
  2. 2.Institut für Optimierung und Operations ResearchUniversität UlmUlmGermany
  3. 3.Instituto de ComputaçãoUniversidade Federal FluminenseNiteróiBrazil

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