@techreport{TR-IC-02-04,
  number = {IC-02-04},
  author = {M. H. {de Carvalho} and C. L. Lucchesi and U. S. R. Murty},
  title = {Graphs with Independent Perfect Matchings},
  month = {March},
  year = {2002}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 32 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      A graph with at least two vertices is {\em matching covered} if
      it is connected and each edge lies in some perfect matching. A
      matching covered graph $G$ is {\em extremal} if the number of
      perfect matchings of $G$ is equal to the dimension of the
      lattice spanned by the set of incidence vectors of perfect
      matchings of $G$. We first establish several basic properties of
      extremal matching covered graphs. In particular, we show that
      every extremal brick may be obtained by splicing graphs whose
      underlying simple graphs are odd wheels. Then, using some of our
      previously published results[*] we find all the extremal cubic
      matching covered graphs.
    \par
      [*] {\em On a Conjecture of Lovász Concerning Bricks}:
      I.~{\em The Characteristic of a Matching Covered Graph}.
      II.~{\em Bricks of Finite Characteristic}. To appear in 
      {\em J. of Combinatorial Theory}, Series B; published
      electronically on Feb/2002.
  }
}