Clique Graph Recognition Is NP-Complete

  • L. Alcón
  • L. Faria
  • C. M. H. de Figueiredo
  • M. Gutierrez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4271)


A complete set of a graph G is a subset of V inducing a complete subgraph. A clique is a maximal complete set. Denote by \({\mathcal{C}}(G)\) the clique family of G. The clique graph of G, denoted by K(G), is the intersection graph of \(\mathcal{{C}}(G)\). Say that G is a clique graph if there exists a graph H such that G=K(H). The clique graph recognition problem asks whether a given graph is a clique graph. A sufficient condition was given by Hamelink in 1968, and a characterization was proposed by Roberts and Spencer in 1971. We prove that the clique graph recognition problem is NP-complete.


Planar Graph Complete Graph Intersection Graph Truth Assignment Nonempty Intersection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • L. Alcón
    • 1
  • L. Faria
    • 2
  • C. M. H. de Figueiredo
    • 3
  • M. Gutierrez
    • 1
  1. 1.Departamento de MatemáticaUNLPArgentina
  2. 2.Departamento de MatemáticaFFP, UERJBrazil
  3. 3.Instituto de Matemática and COPPEUFRJBrazil

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