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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.)
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