  If $H$ is (or is isomorphic to) a subgraph of $G$, $H$ is said to {\it
divide} $G$ if there is an edge-decomposition of $G$ by copies of $E(H)$, the
edge set of $H$. A more restrictive version of this is when there is a subgroup
${\cal H}$ of {\rm Aut} $(G)$, the automorphism group of $G$, such that the
copies of $E(H)$ are the translates of $E(H)$ by the elements of ${\cal H}$. In
a paper by the second author, this situation was described by saying that $H$,
or more precisely $E(H)$, is a {\it fundamental} set for $G$. Many authors have
studied the notion of divisibility for various graphs, and in particular for
various subgraphs of hypercubes, such as paths, trees, and cycles. We continue
such a study in this paper; both for divisibilty, and, when possible, for
fundamental sets. The final section of the paper lists our main results.
