Decomposition of hypercube graphs into paths and cycles of length four

Decomposition of hypercube graphs into paths and cycles of length four

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By a [Formula: see text]-decomposition of a graph G, we mean a Shirt 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 [Formula: see text]-decomposition of the n-dimensional hypercube graph Qn for gtech brush bar 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, [Formula: see text] and n is odd, [Formula: see text].