Geodesic
Note on cyclic decompositions of complete bipartite graphs into cubes
Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 2, pp. 219-227.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: hypercubes, bipartite graphs, factorization 
@article{DMGT_1999_19_2_a7,
     author = {Fron\v{c}ek, Dalibor},
     title = {Note on cyclic decompositions of complete bipartite graphs into cubes},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {219--227},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_1999_19_2_a7/}
}
TY  - JOUR
AU  - Fronček, Dalibor
TI  - Note on cyclic decompositions of complete bipartite graphs into cubes
JO  - Discussiones Mathematicae. Graph Theory
PY  - 1999
SP  - 219
EP  - 227
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_1999_19_2_a7/
LA  - en
ID  - DMGT_1999_19_2_a7
ER  - 
%0 Journal Article
%A Fronček, Dalibor
%T Note on cyclic decompositions of complete bipartite graphs into cubes
%J Discussiones Mathematicae. Graph Theory
%D 1999
%P 219-227
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_1999_19_2_a7/
%G en
%F DMGT_1999_19_2_a7
Fronček, Dalibor. Note on cyclic decompositions of complete bipartite graphs into cubes. Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 2, pp. 219-227. http://geodesic.mathdoc.fr/item/DMGT_1999_19_2_a7/

[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)4:151::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.