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Factorizations of complete multipartite graphs into generalized cubes. (English) Zbl 0940.05055

The generalized cube \(Q(K_k, d)\) is the Cartesian product of \(d\) copies of \(K_k\) (complete graphs on \(k\) vertices). The authors investigate the decomposition of the complete multipartite graph \(K_{k^j \times k^{n-j}}\) into factors that are vertex-disjoint unions of generalized cubes \(Q(K_k, d_i)\), where \(d_i\) may be different in different factors. Some results about \(Q(K_k,d)\)-factorizations are proven when \(k\) is a prime power.

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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References:

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