Decomposition of complete graphs into 5-cubes
Necessary conditions for the complete graph on n vertices to have a decomposition into 5‐cubes are that 5 divides n − 1 and 80 divides n(n − 1)/2. These are known to be sufficient when n is odd. We prove them also sufficient for n even, thus completing the spectrum problem for the 5‐cube and lending...
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| Veröffentlicht in: | Journal of combinatorial designs 2006-03, Vol.14 (2), p.159-166 |
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| container_end_page | 166 |
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| container_issue | 2 |
| container_start_page | 159 |
| container_title | Journal of combinatorial designs |
| container_volume | 14 |
| creator | Bryant, D. El-Zanati, S. I. Maenhaut, B. Vanden Eynden, C. |
| description | Necessary conditions for the complete graph on n vertices to have a decomposition into 5‐cubes are that 5 divides n − 1 and 80 divides n(n − 1)/2. These are known to be sufficient when n is odd. We prove them also sufficient for n even, thus completing the spectrum problem for the 5‐cube and lending further weight to a long‐standing conjecture of Kotzig. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 159–166, 2006 |
| doi_str_mv | 10.1002/jcd.20066 |
| format | Article |
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| subjects | cube decomposition Kotzig Conjecture |
| title | Decomposition of complete graphs into 5-cubes |
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