On the Ramsey multiplicity of complete graphs
β Scribed by David Conlon
- Book ID
- 113046137
- Publisher
- Springer-Verlag
- Year
- 2012
- Tongue
- English
- Weight
- 178 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A new upper bound is given for the cycle-complete graph Ramsey number r(Cm, K,,), the smallest order for a graph which forces it to contain either a cycle of order m or a set of n independent vertices. Then, another cycle-complete graph Ramsey number is studied, namely r(sCm, K,) the smallest order
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
A paopm graph G has no isolated points. I t s R m e y r u m b a r ( G ) i s the m i n i m p such that every 2-coloring of the edges of K contains a monochromatic G. The Ramhey m & t @ m y R(G) i s P the r (G) ' With j u s t one exception, namely Kq, we determine R(G) f o r proper graphs u i t h a t