@techreport{TR-DCC-94-11,
  number = {DCC-94-11},
  author = {Carvalho, Marcelo H. and Lucchesi, Cláudio L.},
  title = {Matching Covered Graphs and Subdivisions of {$K_4$} and {$\overline{C_6}$}},
  month = {December},
  year = {1994}, 
  institution = {Department of Computer Science, University of Campinas},
  note = {In English, 5 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      We give a very simple proof that every non-bipartite matching
      covered graph contains a nice subgraph that is an odd subdivision
      of $K_4$ or $\overline{C_6}$.  It follows immediately that every
      brick different from $K_4$ and $\overline{C_6}$ has an edge whose
      removal preserves the matching covered property.  These are
      classical and very useful results due to Lovász.
  }
}