Decompositions Into Four Cubes
β Scribed by Ko, C.
- Book ID
- 120100065
- Publisher
- Oxford University Press
- Year
- 1936
- Tongue
- English
- Weight
- 52 KB
- Volume
- s1-11
- Category
- Article
- ISSN
- 0024-6107
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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
In this paper, we explore the following question: Given integers d and k, is it possible to subdivide a d-dimensional cube into k smaller d-dimensional cubes? In particular, we investigate bounds on the integer c(d) which is the smallest integer for which it is possible to subdivide the d-cube into