## Abstract Graph __G__ is a (__k__,β__p__)βgraph if __G__ does not contain a complete graph on __k__ vertices __K__~__k__~, nor an independent set of order __p__. Given a (__k__,β__p__)βgraph __G__ and a (__k__,β__q__)βgraph __H__, such that __G__ and __H__ contain an induced subgraph isomorphic t
A Note on Constructive Lower Bounds for the Ramsey Numbers R(3, t)
β Scribed by F.R.K. Chung; R. Cleve; P. Dagum
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 189 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
## Abstract Let __r(k__) denote the least integer __n__βsuch that for any graph __G__ on __n__ vertices either __G__ or its complement G contains a complete graph __K__~k~ on __k__ vertices. in this paper, we prove the following lower bound for the Ramsey number __r(k__) by explicit construction: _
## 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 β8/3__n__β. Here we prove that __r__(__K__~3~,__G__) β©½ β5/2__n__β β1 for __n_