Decomposition of complete graphs into 5-cubes

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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of combinatorial designs 2006-03, Vol.14 (2), p.159-166
Hauptverfasser: Bryant, D., El-Zanati, S. I., Maenhaut, B., Vanden Eynden, C.
Format: Artikel
Sprache:eng
Schlagworte:
cube decomposition
Kotzig Conjecture
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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
ISSN:1063-8539
1520-6610
DOI:10.1002/jcd.20066