## $$C_5$$-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.

### MSC:

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