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Cube factorizations of complete graphs

✍ Scribed by Peter Adams; Darryn Bryant; Barbara Maenhaut

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
94 KB
Volume
12
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

A cube factorization of the complete graph on n vertices, K~n~, is a 3‐factorization of K~n~ in which the components of each factor are cubes. We show that there exists a cube factorization of K~n~ if and only if n ≡ 16 (mod 24), thus providing a new family of uniform 3‐factorizations as well as a partial solution to an open problem posed by Kotzig in 1979. © 2004 Wiley Periodicals, Inc.

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