## 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 into short even cycles
β Scribed by Benjamin R. Smith; Nicholas J. Cavenagh
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 145 KB
- Volume
- 19
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
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
We prove that any complete multipartite graph with parts of even size can be decomposed into closed trails with prescribed even lengths.
## Abstract In this article, it is proved that for each even integer __m__β©Ύ4 and each admissible value __n__ with __n__>2__m__, there exists a cyclic __m__βcycle system of __K__~__n__~, which almost resolves the existence problem for cyclic __m__βcycle systems of __K__~__n__~ with __m__ even. Β© 201
## Abstract For all odd integers __n__ββ₯β1, let __G~n~__ denote the complete graph of order __n__, and for all even integers __n__ββ₯β2 let __G~n~__ denote the complete graph of order __n__ with the edges of a 1βfactor removed. It is shown that for all nonβnegative integers __h__ and __t__ and all p
## Abstract We determine the necessary and sufficient conditions for the existence of a decomposition of the complete graph of even order with a 1βfactor added into cycles of equal length. Β© 2003 Wiley Periodicals, Inc. J Combin Designs 11: 170β207, 2003; Published online in Wiley InterScience (www