  We consider edge decompositions of the $n$-dimensional hypercube $Q_n$ into
isomorphic copies of a given graph $H$. While a number of results are known
about decomposing $Q_n$ into graphs from various classes, the simplest cases of
paths and cycles of a given length are far from being understood. A conjecture
of Erde asserts that if $n$ is even, $\ell < 2^n$ and $\ell$ divides the number
of edges of $Q_n$, then the path of length $\ell$ decomposes $Q_n$. Tapadia et
al.\ proved that any path of length $2^mn$, where $2^m<n$, satisfying these
conditions decomposes $Q_n$. Here, we make progress toward resolving Erde's
conjecture by showing that cycles of certain lengths up to $2^{n+1}/n$
decompose $Q_n$. As a consequence, we show that $Q_n$ can be decomposed into
copies of any path of length at most $2^{n}/n$ dividing the number of edges of
$Q_n$, thereby settling Erde's conjecture up to a linear factor.
