# Decomposing complete graphs into cubes

Saad I. El-Zanati; C. Vanden Eynden

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 1, page 141-147
- ISSN: 2083-5892

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topSaad I. El-Zanati, and C. Vanden Eynden. "Decomposing complete graphs into cubes." Discussiones Mathematicae Graph Theory 26.1 (2006): 141-147. <http://eudml.org/doc/270613>.

@article{SaadI2006,

abstract = {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.},

author = {Saad I. El-Zanati, C. Vanden Eynden},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph decomposition; graph factorization; d-cube},

language = {eng},

number = {1},

pages = {141-147},

title = {Decomposing complete graphs into cubes},

url = {http://eudml.org/doc/270613},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Saad I. El-Zanati

AU - C. Vanden Eynden

TI - Decomposing complete graphs into cubes

JO - Discussiones Mathematicae Graph Theory

PY - 2006

VL - 26

IS - 1

SP - 141

EP - 147

AB - 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.

LA - eng

KW - graph decomposition; graph factorization; d-cube

UR - http://eudml.org/doc/270613

ER -

## References

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