Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Edge Decompositions of Hypercubes by Paths and by Cycles   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.

12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph