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On the clique operator

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

Abstract

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.

Keywords

Recognition Problem Intersection Graph Subgraph Isomorphic Central Vertex Simplicial Vertex 
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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References

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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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