## Abstract Graham and Pollak [3] proved that __n__ โ1 is the minimum number of edgeโdisjoint 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 the decomposition of kn into complete bipartite graphs
โ Scribed by H. Tverberg
- Publisher
- John Wiley and Sons
- Year
- 1982
- Tongue
- English
- Weight
- 76 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
Abstract
A short proof is given of the impossibility of decomposing the complete graph on n vertices into nโ2 or fewer complete bipartite graphs.
๐ SIMILAR VOLUMES
The pagenumber p(G) of a graph G is defined as the smallest n such that G can be embedded in a book with n pages. We give an upper bound for the pagenumber of the complete bipartite graph K m, n . Among other things, we prove p(K n, n ) w2nร3x+1 and p(K wn 2 ร4x, n ) n&1. We also give an asymptotic
## Abstract Necessary conditions for the complete graph on __n__ vertices to have a decomposition into 5โcubes are that 5 divides __n__โโโ1 and 80 divides __n__(__n__โโโ1)/2. These are known to be sufficient when __n__ is odd. We prove them also sufficient for __n__ even, thus completing the spectr
## Abstract Generalizing the wellโknown concept of an __i__โperfect cycle system, Pasotti [Pasotti, in press, Australas J Combin] defined a ฮโdecomposition (ฮโfactorization) of a complete graph __K__~__v__~ to be __iโperfect__ if for every edge [__x__, __y__] of __K__~__v__~ there is exactly one bl
## Abstract For all odd integers __n__โโฅโ1, let __G~n~__ denote the complete graph of order __n__, and for all even integers __n__โโฅโ2 let __G~n~__ denote the complete graph of order __n__ with the edges of a 1โfactor removed. It is shown that for all nonโnegative integers __h__ and __t__ and all p