𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Tree-complete graph ramsey numbers

✍ Scribed by V. Chvátal


Publisher
John Wiley and Sons
Year
1977
Tongue
English
Weight
50 KB
Volume
1
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis


Abstract

The ramsey number of any tree of order m and the complete graph of order n is 1 + (m − 1)(n − 1).


📜 SIMILAR VOLUMES


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).

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

The ramsey numbers for stripes and one c
✍ Peter Lorimer 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 244 KB 👁 1 views

The Ramsey numbers M,,, n,P,, ..., n,P,), p > 2, are calculated. ## 1. Introduction One class of generalized Ramsey numbers that are known exactly are those for the graphs nP2 which consist of n disjoint paths of length 2; E. J. Cockayne and the author proved in 111 that d r(nlp2, ..., n d P 2 ) =

All cycle-complete graph Ramsey numbers
✍ Ingo Schiermeyer 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 122 KB

## Abstract The cycle‐complete graph Ramsey number __r__(__C~m~__, __K~n~__) is the smallest integer __N__ such that every graph __G__ of order __N__ contains a cycle __C~m~__ on __m__ vertices or has independence number α(__G__) ≥ __n__. It has been conjectured by Erdős, Faudree, Rousseau and Sche

Local and meank-Ramsey numbers for compl
✍ Schelp, R. H. 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 67 KB 👁 2 views

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.