𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A survey of bounds for classical Ramsey numbers

✍ Scribed by F. R. K. Chung; C. M. Grinstead

Publisher
John Wiley and Sons
Year
1983
Tongue
English
Weight
546 KB
Volume
7
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

This paper is a survey of the methods used for determining exact values and bounds for the classical Ramsey numbers in the case that the sets being colored are two‐element sets. Results concerning the asymptotic behavior of the Ramsey functions R(k,l) and R~m~(k) are also given.

πŸ“œ SIMILAR VOLUMES

New lower bounds for seven classical Ram
New lower bounds for seven classical Ramsey numbers
✍ Kang Wu; Wenlong Su; Haipeng Luo; Xiaodong Xu πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 346 KB

New lower bounds for seven classical Ramsey numbers are obtained by considering some circulant graphs G n (A i ) with n β‰₯ 142 whose orders might be either prime or not. The results are

Lower bounds for lower Ramsey numbers
Lower bounds for lower Ramsey numbers
✍ Ralph Faudree; Ronald J. Gould; Michael S. Jacobson; Linda Lesniak πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 310 KB πŸ‘ 1 views

## Abstract For any graph __G__, let __i__(__G__) and ΞΌ;(__G__) denote the smallest number of vertices in a maximal independent set and maximal clique, respectively. For positive integers __m__ and __n__, the lower Ramsey number __s__(__m, n__) is the largest integer __p__ so that every graph of or

New Upper Bounds for Ramsey Numbers
New Upper Bounds for Ramsey Numbers
✍ Y.R Huang; K.M Zhang πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 79 KB

The Ramsey number R(G 1 , G 2 ) is the smallest integer p such that for any graph Some new upper bound formulas are obtained for R(G 1 , G 2 ) and R(m, n), and we derive some new upper bounds for Ramsey numbers here.

Lower bounds for some Ramsey numbers
Lower bounds for some Ramsey numbers
✍ H.L Abbott; E.R Williams πŸ“‚ Article πŸ“… 1974 πŸ› Elsevier Science 🌐 English βš– 145 KB