Decompositions of complete graphs into blown-up cycles Cm[2]Cm[2]

Let Cm[K¯2] stand for a cycle CmCm in which every vertex is replaced by two isolated vertices and every edge by K2,2K2,2. We prove that the complete graph K8mk+1K8mk+1 can be decomposed into graphs isomorphic to Cm[K¯2] for any m≥3m≥3, k>0k>0. Decompositions of complete graphs into certain collections of even cycles are obtained as a corollary. Also some special cases of Alspach Conjecture are solved in this article. All proofs are constructive and use both graph theory and design theory techniques.