Decomposition of hypercube graphs into paths and cycles having k edges - D. Saranya; S. Jeevadoss; V. Nalini; V. Chitra (AKCE International Journal of Graphs and Combinatorics)
For an even graph G and positive integer p, q, and k, the pair (p, q) is an admissible pair if [Formula: see text]. If a graph G admits a decomposition into p copies of [Formula: see text], the path of length k, and q copies of Ck, the cycle of length k, for every admissible pair (p, q), then G has a [Formula: see text]-decomposition. In this paper, we give necessary and sufficient conditions for the existence of a [Formula: see text]-decomposition of n-dimensional hypercube graphs Qn when n is even, [Formula: see text] and [Formula: see text]