# Note on cyclic decompositions of complete bipartite graphs into cubes

Discussiones Mathematicae Graph Theory (1999)

- Volume: 19, Issue: 2, page 219-227
- ISSN: 2083-5892

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topDalibor Fronček. "Note on cyclic decompositions of complete bipartite graphs into cubes." Discussiones Mathematicae Graph Theory 19.2 (1999): 219-227. <http://eudml.org/doc/270319>.

@article{DaliborFronček1999,

abstract = {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.},

author = {Dalibor Fronček},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hypercubes; bipartite graphs; factorization; bipartite graph; cyclic decomposition; cyclic factorization},

language = {eng},

number = {2},

pages = {219-227},

title = {Note on cyclic decompositions of complete bipartite graphs into cubes},

url = {http://eudml.org/doc/270319},

volume = {19},

year = {1999},

}

TY - JOUR

AU - Dalibor Fronček

TI - Note on cyclic decompositions of complete bipartite graphs into cubes

JO - Discussiones Mathematicae Graph Theory

PY - 1999

VL - 19

IS - 2

SP - 219

EP - 227

AB - 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.

LA - eng

KW - hypercubes; bipartite graphs; factorization; bipartite graph; cyclic decomposition; cyclic factorization

UR - http://eudml.org/doc/270319

ER -

## References

top- [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 Zbl0913.05080
- [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.

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