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Decomposing Complete Equipartite Graphs into Closed Trails of Lengthk

✍ Scribed by Benjamin R. Smith

Book ID
106047835
Publisher
Springer Japan
Year
2010
Tongue
English
Weight
154 KB
Volume
26
Category
Article
ISSN
0911-0119

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πŸ“œ SIMILAR VOLUMES

Decomposing complete equipartite graphs
Decomposing complete equipartite graphs into short even cycles
✍ Benjamin R. Smith; Nicholas J. Cavenagh πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 145 KB

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.

Closed trail decompositions of complete
Closed trail decompositions of complete equipartite graphs
✍ Andrea Burgess; Mateja Ε ajna πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 314 KB

## Abstract The complete equipartite graph \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}$K\_m \* {\overline{K\_n}}$\end{document} has mn vertices partitioned into __m__ parts of size __n__, with two vertices adjacent if and only if they are in different parts. In this paper,

Decomposing complete multipartite graphs
Decomposing complete multipartite graphs into closed trails of arbitrary even lengths
✍ Benjamin R. Smith; Selda KüçükΓ§ifΓ§i; Emineşule YazΔ±cΔ± πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 115 KB πŸ‘ 1 views

We prove that any complete multipartite graph with parts of even size can be decomposed into closed trails with prescribed even lengths.

Decomposing complete equipartite graphs
Decomposing complete equipartite graphs into cycles of length 2p
✍ Benjamin R. Smith πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 161 KB πŸ‘ 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