𝔖 Bobbio Scriptorium
✦   LIBER   ✦

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


A note on Ramsey numbers for books
✍ Vladimir Nikiforov; Cecil C. Rousseau 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 87 KB 👁 1 views

## 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 irredundant Ramsey numbers for graphs
✍ Johannes H. Hattingh 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 248 KB

## 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

On Book-Complete Graph Ramsey Numbers
✍ Yusheng Li; C.C. Rousseau 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 274 KB

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

On Regressive Ramsey Numbers
✍ Peter Floodstrand Blanchard 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 111 KB

## 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

Ramsey Numbers for Matroids
✍ Talmage James Reid 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 233 KB
On ramsey-tuŕan numbers for 3-graphs
✍ A. F. Sidorenko 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 255 KB

## 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