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

Lee, Hung-Chih; Lee, Ming-Ju; Lin, Chiang

Taiwanese J. Math. 13, No. 2A, 393-402 (2009).

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