## Abstract The __book with n pages__ __B__~__n__~ is the graph consisting of __n__ triangles sharing an edge. The __book Ramsey number__ __r__(__B__~__m__~,__B__~__n__~) is the smallest integer __r__ such that either __B__~__m__~ ⊂ __G__ or __B__~__n__~ ⊂ __G__ for every graph __G__ of order __r__
On ramsey numbers for books
✍ Scribed by C. C. Rousseau; J. Sheehan
- Publisher
- John Wiley and Sons
- Year
- 1978
- Tongue
- English
- Weight
- 479 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
For n = 1, 2, . . . , let 6, = K2+ K,,. We pose the problem of determining the Ramsey numbers r(&, B,) and demonstrate that in many cases critical colorings are available from known examples of strongly regular graphs.
📜 SIMILAR VOLUMES
## Abstract The irredundant Ramsey number __s(m, n)__ is the smallest p such that in every two‐coloring of the edges of __K~p~__ using colors red (__R__) and blue (__B__), either the blue graph contains an __m__‐element irredundant set or the red graph contains an __n__‐element irredundant set. We
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 xÂx) (x Ä ). From this result we find that the book-complete graph Ramsey number satisfies r(B m , K n ) mn 2 Âlog(nÂe). I
## for my mentors don bonar and gerald thompson We prove the following relation between regressive and classical Ramsey numbers ¼ 8; R 4 reg ð6Þ ¼ 15; and R 5 reg ð7Þ536: We prove that R 2 xþk ð4Þ42 kþ1 ð3 þ kÞ À ðk þ 1Þ; and use this to compute R 2 reg ð5Þ ¼ 15: Finally, we provide the bounds 19
## Abstract For every __r__‐graph __G__ let π(__G__) be the minimal real number ϵ such that for every ϵ < 0 and __n__ ϵ __n__~0~(λ, __G__) every __R__‐graph __H__ with __n__ vertices and more than (π + ϵ)(nr) edges contains a copy of __G__. The real number λ(__G__) is defined in the same way, addin