Note on cyclic decompositions of complete bipartite graphs into cubes

• Autorzy: Dalibor Fronček
• Języki publikacji: EN

Abstrakty

EN

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 $K_{d2^{d-1}, d2^{d-2}}$. We improve this result and show that also $K_{d2^{d-2}, d2^{d-2}}$ allows a cyclic decomposition into $Q_d$. We also present a cyclic factorization of $K_{8,8}$ into Q₄.

Słowa kluczowe

EN

hypercubes; bipartite graphs; factorization

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1999
• Tom: 19
• Numer: 2
• Strony: 219-227

Daty

wydano

1999

otrzymano

1999-02-03

poprawiono

1999-10-30

Twórcy

autor

Dalibor Fronček

• Department of Applied Mathematics, Technical University Ostrava, 17 listopadu, 708 33 Ostrava, Czech Republic

Bibliografia

• [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
• [2] A. Rosa, On certain valuations of the vertices of a graph, Internat. Sympos. ICC Rome, Dunod, Paris, 1967, 349-355.
• [3] C. Vanden Eynden, Decompositions of complete bipartite graphs, Ars Combinatoria, to appear.

Identyfikatory

DOI

10.7151/dmgt.1096