On Geometric Graph Ramsey Numbers

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 cycle—Complete graph ramsey numbers

✍ P. Erdös; R. J. Faudree; C. C. Rousseau; R. H. Schelp 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 507 KB

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

Fan-complete graph Ramsey numbers

✍ Li, Yusheng; Rousseau, Cecil C. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 427 KB 👁 2 views

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).

Tree-complete graph ramsey numbers

✍ V. Chvátal 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 50 KB

## Abstract The ramsey number of any tree of order __m__ and the complete graph of order __n__ is 1 + (__m__ − 1)(__n__ − 1).

On graphs with linear Ramsey numbers

✍ R. L. Graham; V. Rödl; A. Ruciński 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 141 KB 👁 1 views

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