@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 LovĂˇsz 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.
}
}