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Ramsey numbers r(K3, G) for connected graphs G of order seven

✍ Scribed by Annette Schelten; Ingo Schiermeyer

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
838 KB
Volume
79
Category
Article
ISSN
0166-218X

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✦ Synopsis

The triangle-graph Ramsey numbers are determined for all 814 of the 853 connected graphs of order seven. For the remaining 39 graphs lower and upper bounds are improved.

πŸ“œ SIMILAR VOLUMES

All triangle-graph ramsey numbers for co
All triangle-graph ramsey numbers for connected graphs of order six
✍ R. J. Faudree; C. C. Rousseau; R. H. Schelp πŸ“‚ Article πŸ“… 1980 πŸ› John Wiley and Sons 🌐 English βš– 356 KB

## Abstract The Ramsey numbers __r(K__~3β€²~ __G__) are determined for all connected graphs __G__ of order six.

An upper bound for the Ramsey numbers r(
An upper bound for the Ramsey numbers r(K3,G)
✍ Wayne Goddard; Daniel J. Kleitman πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 372 KB

The Ramsey number r(H, G) is defined as the minimum N such that for any coloring of the edges of the N-vertex complete graph KN in red and blue, it must contain either a ted H or a blue G. In this paper we show that for any graph G without isolated vertices, r(K,, G)< 2qf 1 where G has q edges. In o

An upper bound on the ramsey number R(K3
An upper bound on the ramsey number R(K3, G) depending only on the size of the graph G
✍ A. F. Sidorenko πŸ“‚ Article πŸ“… 1991 πŸ› John Wiley and Sons 🌐 English βš– 135 KB πŸ‘ 1 views

## Abstract Harary stated the conjecture that for any graph __G__ with __n__ edges and without isolated vertices __r__(__K__~3~,__G__) β©½ 2__n__ + 1. ErdΓΆs, Faudree, Rousseau, and Schelp proved that __r__(__K__~3~,__G__) β©½ ⌈8/3__n__βŒ‰. Here we prove that __r__(__K__~3~,__G__) β©½ ⌊5/2__n__βŒ‹ βˆ’1 for __n_