Note on cyclic decompositions of complete bipartite graphs into cubes

Dalibor Fronček

Discussiones Mathematicae Graph Theory, Tome 19 (1999), p. 219-227 / Harvested from The Polish Digital Mathematics Library

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Résumé

So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes $Q_{d}$ of a given dimension d was $K_{d 2^{d - 1}, d 2^{d - 2}}$ . We improve this result and show that also $K_{d 2^{d - 2}, d 2^{d - 2}}$ allows a cyclic decomposition into $Q_{d}$ . We also present a cyclic factorization of $K_{8, 8}$ into Q₄.

Publié le : 1999-01-01

Zbl 0958.05110

EUDML-ID : urn:eudml:doc:270319

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Dalibor Fronček. Note on cyclic decompositions of complete bipartite graphs into cubes. Discussiones Mathematicae Graph Theory, Tome 19 (1999) pp. 219-227. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1096/

Bibliographie

[000] [1] S. El-Zanati and C. Vanden Eynden, Decompositions of K_{m,n} into cubes, J. Comb. Designs 4 (1) (1996) 51-57, doi: 10.1002/(SICI)1520-6610(1996)4:1<51::AID-JCD5>3.0.CO;2-Z | Zbl 0913.05080

[001] [2] A. Rosa, On certain valuations of the vertices of a graph, Internat. Sympos. ICC Rome, Dunod, Paris, 1967, 349-355.

[002] [3] C. Vanden Eynden, Decompositions of complete bipartite graphs, Ars Combinatoria, to appear.