@techreport{TR-IC-06-02,
  number = {IC-06-02},
  author = {Sheila Morais de Almeida and Célia Picinin de Mello and
            Anamaria Gomide},
  title = {On the representation of a {PI-Graph}},
  month = {February},
  year = {2006}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 9 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       Consider two parallel lines (denoted by $r_1$ and $r_2$).  A
       graph is a PI graph (Point-Interval graph) if it is an
       intersection graph of a family F of triangles between $r_1$ and
       $r_2$ such that each triangle has an interval with two
       endpoints on $r_1$ and a vertex (a point) on $r_2$. The family
       F is the PI representation of G. The PI graphs are an extension
       of interval and permutation graphs and they form a subclass of
       trapezoid graphs.  In this paper, we characterize the PI graphs
       in terms of its trapezoid representation. Also we show how to
       construct a family of trapezoid graphs but not PI graphs from a
       trapezoid representation of a known graph in this class.
  }
}