## 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
✦ LIBER ✦
Decomposing complete multipartite graphs into closed trails of arbitrary even lengths
✍ Scribed by Benjamin R. Smith; Selda Küçükçifçi; Emineşule Yazıcı
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 115 KB
- Volume
- 19
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
✦ Synopsis
We prove that any complete multipartite graph with parts of even size can be decomposed into closed trails with prescribed even lengths.
📜 SIMILAR VOLUMES
Decomposing complete equipartite graphs
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Benjamin R. Smith
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Decomposing complete equipartite graphs
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Benjamin R. Smith
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## 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 λ are positive integers with __n__ ≥ 3, λ≥ 3 and __n__ and λ both odd