Isomorphic path decompositions of $$\lambda K_{n,n,n}(\lambda K^*_{n,n,n})$$ for odd $$n$$.(English)Zbl 1175.05070

Summary: The isomorphic path decompositions of $$\lambda$$-fold balanced complete tripartite graphs $$\lambda K_{n,n,n}$$ and $$\lambda$$-fold balanced complete tripartite digraphs $$\lambda K_{n,n,n}^*$$ are investigated for odd $$n$$. We prove that the obvious necessary conditions for such decompositions in the undirected case are also sufficient; we also provide sufficient conditions for the directed case.

MSC:

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