  A cubical polytope is a polytope with all its facets being combinatorially
equivalent to cubes. We deal with the connectivity of the graphs of cubical
polytopes. We first establish that, for any $d\ge 3$, the graph of a cubical
$d$-polytope with minimum degree $\delta$ is $\min\{\delta,2d-2\}$-connected.
Second, we show, for any $d\ge 4$, that every minimum separator of cardinality
at most $2d-3$ in such a graph consists of all the neighbours of some vertex
and that removing the vertices of the separator from the graph leaves exactly
two components, with one of them being the vertex itself.
