  Given a graph $G=(V,E)$ and a set $S \subseteq \binom{V}{2}$ of terminal
pairs, the minimum multicut problem asks for a minimum edge set $\delta
\subseteq E$ such that there is no $s$-$t$-path in $G -\delta$ for any
$\{s,t\}\in S$. For $|S|=1$ this is the well known $s$-$t$-cut problem, but in
general the minimum multicut problem is NP-complete, even if the input graph is
a tree. The multicut polytope $\text{MultC}^\square (G,S)$ is the convex hull
of all multicuts in $G$; the multicut dominant is given by
$\text{MultC}(G,S)=\text{MultC}^\square (G,S)+\mathbb{R}^E$. The latter is the
relevant object for the minimization problem. While polyhedra associated to
several cut problems have been studied intensively there is only little
knowledge for multicut.
  We investigate properties of the multicut dominant and in particular derive
results on liftings of facet-defining inequalities. This yields a
classification of all facet-defining path- and edge inequalities. Moreover, we
investigate the effect of graph operations such as node splitting, edge
subdivisions, and edge contractions on the multicut-dominant and its
facet-defining inequalities. In addition, we introduce facet-defining
inequalities supported on stars, trees, and cycles and show that the former two
can be separated in polynomial time when the input graph is a tree.
