## Abstract As a consequence of our main result, a theorem of Schrijver and Seymour that determines the zero sum Ramsey numbers for the family of all __r__βhypertrees on __m__ edges and a theorem of Bialostocki and Dierker that determines the zero sum Ramsey numbers for __r__βhypermatchings are com
Ramsey numbers for multiple copies of complete graphs
β Scribed by P. J. Lorimer; R. J. Segedin
- Publisher
- John Wiley and Sons
- Year
- 1978
- Tongue
- English
- Weight
- 107 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
It is shown that if G and H are arbitrary fixed graphs and n is sufficiently large, then Also, we prove that r ( K 1 +F, K,) 5 (m+o(l))&(n -+ GO) for any forest Fwhose largest component has m edges. Thus r(Fe, K,) 5 (1 + o(l))&, where Fe = K1 + CK2. We conjecture that r(Fe, K,) -&(n + cm).
## Abstract The ramsey number of any tree of order __m__ and the complete graph of order __n__ is 1 + (__m__ β 1)(__n__ β 1).
This paper establishes that the local k-Ramsey number R(K m , k -loc) is identical with the mean k-Ramsey number R(K m , k -mean). This answers part of a question raised by Caro and Tuza.
It is shown that a graph of order N and average degree d that does not contain the book B m =K 1 +K 1, m as a subgraph has independence number at least Nf (d ), where f (x)t(log xΓx) (x Γ ). From this result we find that the book-complete graph Ramsey number satisfies r(B m , K n ) mn 2 Γlog(nΓe). I