## Abstract A short proof is given of the impossibility of decomposing the complete graph on __n__ vertices into __n__β2 or fewer complete bipartite graphs.
The toroidal splitting number of the complete graph Kn
β Scribed by Nora Hartsfield
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 582 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## 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
## Abstract We prove that for every prime number __p__ and odd __m__>1, as __s__ββ, there are at least __w__ face 2βcolorable triangular embeddings of __K__~__w, w, w__~, where __w__ = __m__Β·__p__^__s__^. For both orientable and nonorientable embeddings, this result implies that for infinitely many
Erd6s. P. and C.C. Rousseau, The size Ramsey number of a complete bipartite graph, Discrete Mathematics 113 (1993) 259-262. In this note we prove that the (diagonal) size Ramsey number of K,,.,, is bounded below by $2'2".
The aim of this paper is to determine the maximal number of induced K(t, t) subgraphs in graphs of given order and in graphs of given size. Given a graph G and a natural number t, denote by ft(G) the number of induced subgraphs of G isomorphic to K(t, t). Our notation is that of ; in particular, K(