Decomposing complete graphs into cubes
Discussiones Mathematicae Graph Theory, Tome 26 (2006) no. 1, p. 141.

Voir la notice de l'article dans European Digital Mathematics Library

This paper concerns when the complete graph on n vertices can be decomposed into d-dimensional cubes, where d is odd and n is even. (All other cases have been settled.) Necessary conditions are that n be congruent to 1 modulo d and 0 modulo 2 d . These are known to be sufficient for d equal to 3 or 5. For larger values of d, the necessary conditions are asymptotically sufficient by Wilson’s results. We prove that for each odd d there is an infinite arithmetic progression of even integers n for which a decomposition exists. This lends further weight to a long-standing conjecture of Kotzig.
Classification : 05C30, 05C70
Mots-clés : graph decomposition, graph factorization, d-cube 
@article{DMGT_2006__26_1_270613,
     author = {Saad I. El-Zanati and C. Vanden Eynden},
     title = {Decomposing complete graphs into cubes},
     journal = {Discussiones Mathematicae Graph Theory},
     pages = {141},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2006},
     zbl = {1131.05072},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DMGT_2006__26_1_270613/}
}
TY  - JOUR
AU  - Saad I. El-Zanati
AU  - C. Vanden Eynden
TI  - Decomposing complete graphs into cubes
JO  - Discussiones Mathematicae Graph Theory
PY  - 2006
SP  - 141
VL  - 26
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DMGT_2006__26_1_270613/
LA  - en
ID  - DMGT_2006__26_1_270613
ER  - 
%0 Journal Article
%A Saad I. El-Zanati
%A C. Vanden Eynden
%T Decomposing complete graphs into cubes
%J Discussiones Mathematicae Graph Theory
%D 2006
%P 141
%V 26
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DMGT_2006__26_1_270613/
%G en
%F DMGT_2006__26_1_270613
Saad I. El-Zanati; C. Vanden Eynden. Decomposing complete graphs into cubes. Discussiones Mathematicae Graph Theory, Tome 26 (2006) no. 1, p. 141. https://geodesic-test.mathdoc.fr/item/DMGT_2006__26_1_270613/