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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