On the clique operator

  • Marisa Gutierrez
  • JoÃo Meidanis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1380)


The clique operator K maps a graph G into its clique graph, which is the intersection graph of the (maximal) cliques of G. Among all the better studied graph operators, K seems to be the richest one and many questions regarding it remain open. In particular, it is not known whether recognizing a clique graph is in P. In this note we describe our progress toward answering this question. We obtain a necessary condition for a graph to be in the image of K in terms of the presence of certain subgraphs A and B. We show that being a clique graph is not a property that is maintained by addition of twins. We present a result involving distances that reduces the recognition problem to graphs of diameter at most two. We also give a constructive characterization of K−1(G) for a fixed but generic G.


Recognition Problem Intersection Graph Subgraph Isomorphic Central Vertex Simplicial Vertex 
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  1. 1.
    C. Berge. Hypergraphes. Gauthier-Villars, Paris, 1987.Google Scholar
  2. 2.
    M. Gutierrez. Intersection graphs and clique application. Unpublished manuscript.Google Scholar
  3. 3.
    R. Hamelink. A partial characterization of clique graphs. J. Combin. Theory, 5:192–197, 1968.zbMATHMathSciNetGoogle Scholar
  4. 4.
    E. Prisner. Hereditary clique-helly graphs. J. Comb. Math. Comb. Comput., 1991.Google Scholar
  5. 5.
    F. S. Roberts and J. H. Spencer. A characterization of clique graphs. J. Combin. Theory, Series B, 10:102–108, 1971.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Marisa Gutierrez
    • 1
  • JoÃo Meidanis
    • 2
  1. 1.Departamento de MatemáticaUniversidad Nacional de La PlataLa PlataArgentina
  2. 2.Institute of ComputingUniversity of CampinasCampinas SPBrazil

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