Decompositions into cubes of primes (II)
β Scribed by Gupta, Hansraj
- Book ID
- 112976500
- Publisher
- Springer-Verlag
- Year
- 1936
- Tongue
- English
- Weight
- 312 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0370-0089
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π SIMILAR VOLUMES
For a complete bipartite graph to be decomposable into isomorphic cubes, certain conditions on the number of cube and bipartition vertices must hold. We prove these necessary conditions sufficient in some cases. For cubes of fixed dimension d (indeed for d-regular bipartite graphs in general) we sho
## Abstract Necessary conditions for the complete graph on __n__ vertices to have a decomposition into 5βcubes are that 5 divides __n__βββ1 and 80 divides __n__(__n__βββ1)/2. These are known to be sufficient when __n__ is odd. We prove them also sufficient for __n__ even, thus completing the spectr