@techreport{TR-IC-98-24,
  number = {IC-98-24},
  author = {Marcelo H. {de Carvalho} and Cláudio L. Lucchesi and U. S. R. Murty},
  title = {On a Conjecture of {L}ovász Concerning Bricks},
  month = {July},
  year = {1998}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 53 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      In 1987,  Lovász  conjectured  that  every brick   $G$  different from
      $K_{4}$,  $\overline{C}_{6}$, and the Petersen   graph has an edge $e$
      such that $G-e$  is a matching covered graph  with exactly  one brick.
      Lovász and Vempala announced a proof of this conjecture in 1994. Their
      paper is under  preparation. We present  here an independent  proof of
      their theorem.  We  shall in  fact prove  that   if $G$ is  any  brick
      different from $K_{4}$  and $\overline{C}_{6}$ and  does not  have the
      Petersen graph as its underlying simple graph, then it has an edge $e$
      such that $G-e$  is a matching  covered graph with exactly one  brick,
      with the additional property that the  underlying simple graph of that
      one  brick is different from the  Petersen  graph.  Our proof involves
      establishing an interesting new property of the Petersen graph.
  }
}