Decomposing toroidal graphs into circuits and edges
β Scribed by Baogang Xu; Lusheng Wang
- Book ID
- 108112498
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 215 KB
- Volume
- 148
- Category
- Article
- ISSN
- 0166-218X
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π SIMILAR VOLUMES
In this article we find necessary and sufficient conditions to decompose a complete equipartite graph into cycles of uniform length, in the case that the length is both even and short relative to the number of parts.
Let It'Qn; r) denote the complete s-partite graph Kin, n, '.., n). it is shown hzre that for all even n(r -I) 2, Kfn; P) is the union of n(r -'I)/2 of its Hamilton circrlits which are mutually edge-disjoint, and for all odd nfr -1) 3 1, K(n; P) is the union of b(P -f) -r,,rs f l t ii o I s amilton c
## Abstract It is an open problem to determine whether a complete equipartite graph $K\_m\*{\overline{K}}\_n$ (having __m__ parts of size __n__) admits a decomposition into cycles of arbitrary fixed length $k$ whenever __m__, __n__, and __k__ satisfy the obvious necessary conditions for the existen