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Decomposition of complete graphs into 5-cubes

✍ Scribed by D. Bryant; S. I. El-Zanati; B. Maenhaut; C. Vanden Eynden

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 116 KB
Volume: 14
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20066

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✦ Synopsis

Abstract

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

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