## 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
Decomposing complete equipartite graphs into odd square-length cycles: Number of parts even
β Scribed by Benjamin R. Smith; Nicholas Cavenagh
- Book ID
- 113567609
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 268 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
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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.
## 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
We prove that any complete multipartite graph with parts of even size can be decomposed into closed trails with prescribed even lengths.