  We are given a graph $G$, an independant set $\mathcal{S} \subset V(G)$ of
\emph{terminals}, and a function $w:V(G) \to \mathbb{N}$. We want to know if
the maximum $w$-packing of vertex-disjoint paths with extremities in
$\mathcal{S}$ is equal to the minimum weight of a vertex-cut separating
$\mathcal{S}$. We call \emph{Mader-Mengerian} the graphs with this property for
each independant set $\mathcal{S}$ and each weight function $w$. We give a
characterization of these graphs in term of forbidden minors, as well as a
recognition algorithm and a simple algorithm to find maximum packing of paths
and minimum multicuts in those graphs.
