\(C_5\)-decompositions of the tensor product of complete graphs. (English) Zbl 1120.05071

Summary: It has been proved that necessary conditions for the existence of \(C_5\)-decomposition of \(K_m\times K_n\) are sufficient, where \(\times\) denotes the tensor product of graphs. Using these necessary and sufficient conditions, it can be shown that every even regular complete multipartite graph \(G\) can be decomposed into 5-cycles if the number of edges of \(G\) is divisible by 5.


05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C38 Paths and cycles