Decomposition of hypercube graphs into paths and cycles of length four

Abstract

By a -decomposition of a graph G, we mean a partition of the edge set of G into p paths of length 4 and q cycles of length 4. In this paper, we give conditions for a -decomposition of the n-dimensional hypercube graph Qn for all possible values of p and q. In particular, we find the necessary and sufficient conditions for such decomposition in Qn when n is even, and n is odd,