Decomposing the complete graph into dodecahedra
β Scribed by P. Adams; D.E. Bryant; A.D. Forbes; T.S. Griggs
- Book ID
- 113757586
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 187 KB
- Volume
- 142
- Category
- Article
- ISSN
- 0378-3758
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π SIMILAR VOLUMES
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.
## 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
We prove the conjecture made by \(\mathrm{O}\). V. Borodin in 1976 that the vertex set of any planar graph can be decomposed into two sets such that one of them induces a 3-degenerate graph and the other induces a 2-degenerate graph. that is, a forest. c. 1995 Academic Press. Inc.