We consider edge decompositions of the n-dimensional hypercube Qn into
isomorphic copies of a given graph H. While a number of results are known
about decomposing Qn 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, ℓ<2n and ℓ divides the number
of edges of Qn, then the path of length ℓ decomposes Qn. Tapadia et
al.\ proved that any path of length 2mn, where 2m<n, satisfying these
conditions decomposes Qn. Here, we make progress toward resolving Erde's
conjecture by showing that cycles of certain lengths up to 2n+1/n
decompose Qn. As a consequence, we show that Qn can be decomposed into
copies of any path of length at most 2n/n dividing the number of edges of
Qn, thereby settling Erde's conjecture up to a linear factor