@techreport{TR-DCC-94-04,
  number = {DCC-94-04},
  author = {de Figueiredo, Celina M. H. and Meidanis, João and de Mello, Célia P.},
  title = {On Edge-Colouring Indifference Graphs},
  month = {June},
  year = {1994}, 
  institution = {Department of Computer Science, University of Campinas},
  note = {In English, 23 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      Vizing's theorem states that the chromatic index $\chi'(G)$ of a
      graph $G$ is either the maximum degree $\Delta(G)$ or $\Delta(G) +
      1$.  A graph $G$ is called {\em overfull\/} if $ |E(G)| >
      \Delta(G) \lfloor{|V(G)|/2}\rfloor$.  A sufficient condition for $\chi'(G)
      =\Delta(G) + 1$ is that $G$ contains an overfull subgraph $H$ with
      $\Delta(H) = \Delta(G)$.  Plantholt proved that this condition is
      necessary for graphs with a universal vertex.  In this paper, we
      conjecture that, for indifference graphs, this is also true.  As
      supporting evidence, we prove this conjecture for general graphs
      with three maximal cliques and with no universal vertex, and for
      indifference graphs with odd maximum degree.  For the latter
      subclass, we prove that $\chi'=\Delta$.
  }
}