## 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
On decomposition of r-partite graphs into edge-disjoint hamilton circuits
β Scribed by Renu Laskar; Bruce Auerbach
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 414 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
Let It'Qn; r) denote the complete s-partite graph Kin, n, '.., n). it is shown hzre that for all even n(r -I) 2, Kfn; P) is the union of n(r -'I)/2 of its Hamilton circrlits which are mutually edge-disjoint, and for all odd nfr -1) 3 1, K(n; P) is the union of b(P -f) -r,,rs f l t ii o I s amilton c.ircuite and a l-factor, all of which are mutually edge-disjoint . denote the complete graph on M vertices and the complete bipartiti graph on 32 vertices with n2 vertices in each vertex respctively. The following properties of Kn and
π SIMILAR VOLUMES
For any positive integer s, an s-partition of a graph G = ( ! -( β¬I is a partition of E into El U E2 U U E k, where 14 = s for 1 I i 5 k -1 and 1 5 1 4 1 5 s and each β¬; induces a connected subgraph of G. We prove (i) if G is connected, then there exists a 2-partition, but not neces-(ii) if G is 2-e