Path and cycle decompositions of complete equipartite graphs: Four parts
β Scribed by Billington, Elizabeth J. (author);Cavenagh, Nicholas J. (author);Smith, Benjamin R. (author)
- Book ID
- 108114074
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 1007 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0012-365X
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## 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,
## Abstract In the study of decompositions of graphs into paths and cycles, the following questions have arisen: Is it true that every graph __G__ has a smallest path (resp. pathβcycle) decomposition __P__ such that every odd vertex of __G__ is the endpoint of exactly one path of __P__? This note g