  We introduce 2-partitionable clutters as the simplest case of the class of
$k$-partitionable clutters and study some of their combinatorial properties. In
particular, we study properties of the rank of the incidence matrix of these
clutters and properties of their minors.
  A well known conjecture of Conforti and Cornu\'ejols
  \cite{ConfortiCornuejols,cornu-book} states: That all the clutters with the
packing property have the max-flow min-cut property, i.e. are mengerian. Among
the general classes of clutters known to verify the conjecture are: balanced
clutters (Fulkerson, Hoffman and Oppenheim \cite{FulkersonHoffmanOppenheim}),
binary clutters (Seymour \cite{Seymour}) and dyadic clutters (Cornu\'ejols,
Guenin and Margot \cite{CornuejolsGueninMargot}). We find a new infinite family
of 2-partitionable clutters, that verifies the conjecture.
  On the other hand we are interested in studying the normality of the Rees
algebra associated to a clutter and possible relations with the Conforti and
Cornu\'ejols conjecture. In fact this conjecture is equivalent to an algebraic
statement about the normality of the Rees algebra \cite{rocky}.
