@techreport{TR-DCC-92-09,
  number = {DCC-92-09},
  author = {Lucchesi, Cláudio L. and de Mello, Célia P. and Szwarcfiter, Jayme L.},
  title = {On Clique-Complete Graphs},
  month = {November},
  year = {1992}, 
  institution = {Department of Computer Science, University of Campinas},
  note = {In English, 10 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      A graph is {\em clique-complete} if no two of its maximal
      cliques are disjoint. A vertex is {\em universal} if it is
      adjacent to all other vertices in the graph.  We prove that
      every clique-complete graph either contains a universal vertex
      or an induced subgraph in an indexed family ${\cal Q} := \{
      Q_{2n + 1}: n \geq 1 \}$, defined in the text. We show that
      this is precisely the family of minimal graphs which are
      clique-complete but have no universal vertices.  The minimality
      used here refers to induced subgraphs.
    \par
      For $n \geq 2$, we show that $Q_{2n + 1}$ is neither
      perfect nor planar. It follows that every planar clique-complete
      graph without a universal vertex contains an induced subgraph
      isomorphic to $Q_3$. A similar result holds for perfect
      clique-complete graphs without universal vertices.  We also
      specialize the latter result for certain classes of perfect
      graphs.
  }
}