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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.)
##### Keywords:
decomposition; path; complete tripartite graph
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