Decomposition of hypercube graphs into paths and cycles of length four

AbstractBy a -decomposition of a graph G, we mean a partition of the edge set of Ginto ppaths of length 4 and qcycles of length 4. In this paper, we give conditions for a -decomposition of the n-dimensional hypercube graph Qnfor all possible values of pand q. In particular, we find the necessary and sufficient conditions for such decomposition in Qnwhen nis even, and nis odd,