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Cube factorizations of complete graphs
Author(s) -
Adams Peter,
Bryant Darryn,
Maenhaut Barbara
Publication year - 2004
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20015
Subject(s) - factorization , combinatorics , cube (algebra) , mathematics , graph , discrete mathematics , algorithm
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.