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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

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✦ 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
✍ Benjamin R. Smith 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 161 KB 👁 1 views

## 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 complete equipartite graphs
✍ Benjamin R. Smith 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 155 KB

## 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