## 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
Decomposing the complete graph into cycles of many lengths
β Scribed by Darryn E. Bryant; Peter Adams
- Publisher
- Springer Japan
- Year
- 1995
- Tongue
- English
- Weight
- 346 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
## Abstract In this article, we introduce a new technique for obtaining cycle decompositions of complete equipartite graphs from cycle decompositions of related multigraphs. We use this technique to prove that if __n__, __m__ and Ξ» are positive integers with __n__ β₯ 3, Ξ»β₯ 3 and __n__ and Ξ» both odd
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.
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