## 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 unifor
Orthogonal factorizations of graphs
✍ Scribed by Haodi Feng; Guizhen Liu
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 92 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Let G be a graph with vertex set V(G) and edge set E(G). Let k~1~, k~2~,…,k~m~ be positive integers. It is proved in this study that every [0,k~1~+…+k~m~−m+1]‐graph G has a [0, k~i~]~1~^m^‐factorization orthogonal to any given subgraph H with m edges. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 267–276, 2002
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