  The paper studies the connectivity properties of facet graphs of simplicial
complexes of combinatorial interest. In particular, it is shown that the facet
graphs of $d$-cycles, $d$-hypertrees and $d$-hypercuts are, respectively,
$(d+1)$, $d$, and $(n-d-1)$-vertex-connected. It is also shown that the facet
graph of a $d$-cycle cannot be split into more than $s$ connected components by
removing at most $s$ vertices. In addition, the paper discusses various related
issues, as well as an extension to cell-complexes.
