On biclique decompositions of complete t-partite graphs
β Scribed by Elizabeth D. Boyer; Bryan L. Shader
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 704 KB
- Volume
- 217
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
In this paper we give a procedure by which Hamiltonian decompositions of the s-partite graph K~.....,~, where (s-1)n is even, can be constructed. For 2t<~s, l<~al<~...<~a~n, we find conditions which are necessary and sufficient for a decomposition of the edge-set of Kal.a2..... ~ into (s-1)n/2 class
## Abstract Graham and Pollak [3] proved that __n__ β1 is the minimum number of edgeβdisjoint complete bipartite subgraphs into which the edges of __K__~__n__~ can be decomposed. Using a linear algebraic technique, Tverberg [2] gives a different proof of that result. We apply his technique to show
A partition of the edge set of a graph H into subsets inducing graphs H,, . . . , H, isomorphic to a graph G is said to be a G-decomposition of H. A G-decomposition of H is resolvable if the set {H,, . . . , H,} can be partitioned into subsets, called resolution classes, such that each vertex of H
In this paDer,
## Abstract We say that two graphs __G__ and __H__ with the same vertex set commute if their adjacency matrices commute. In this article, we show that for any natural number __r__, the complete multigraph __K__ is decomposable into commuting perfect matchings if and only if __n__ is a 2βpower. Also