@techreport{TR-DCC-92-03,
  number = {DCC-92-03},
  author = {Lucchesi, Cláudio L. and Giglio, Maria Cecília M. T.},
  title = {On the Irrelevance of Edge Orientations on the Acyclic Directed Two Disjoint Paths Problem},
  month = {June},
  year = {1992}, 
  institution = {Department of Computer Science, University of Campinas},
  note = {In English, 7 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      Given an undirected graph $G$ and four distinct {\em special
      vertices} $s_1, s_2, t_1, t_2$, the {\em Two Disjoint Paths
      Problem} consists in determining whether there are two disjoint
      paths connecting $s_1$ to $t_1$ and $s_2$ to $t_2$,
      respectively.
    \par
      There is an analogous version of the problem for acyclic
      directed graphs, in which it is required that the two paths be
      directed, as well.
    \par
      The known characterizations for the nonexistence of solutions in
      both problems are, in some sense, the same, which indicates that
      under some weak conditions the edge orientations in the directed
      version are irrelevant.
    \par
      We present the first direct proof of the irrelevance of edge
      orientations.
  }
}