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Many authors have investigated edge decompositions of graphs by the edge setsof isomorphic copies of special subgraphs. For $q$- dimensional hypercubes$Q_q$ various researchers have done this for cer- tain trees, paths, andcycles. In this paper we shall say that "$H$ divides $G$" if $E(G)$ is thedisjoint union of $\{fE(H_i) | H_i \simeq H\}$. Our main result is that for $q$odd and $q < 2^{32}$, the path of length $m$, $P_m$, divides $Q_q$ if and onlyif $m \leq q$ and $m | (q \times 2^{q-1})$.

Edge Decompositions of Hypercubes by Paths