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A note on cycle Ramsey numbers

✍ Scribed by Gary Chartrand; Seymour Schuster


Book ID
107748157
Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
283 KB
Volume
5
Category
Article
ISSN
0012-365X

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## Abstract The __book with n pages__ __B__~__n__~ is the graph consisting of __n__ triangles sharing an edge. The __book Ramsey number__ __r__(__B__~__m__~,__B__~__n__~) is the smallest integer __r__ such that either __B__~__m__~β€‰βŠ‚β€‰__G__ or __B__~__n__~β€‰βŠ‚β€‰__G__ for every graph __G__ of order __r__

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I Retaefltiy, Ramsey numbers have been obtained for several &sses of graphs. In particthey have been studied for hs of low wder, pairs of paths, paks of cycles, and for a . In this paper, th rs atie obtained fair aI3 pa&cycle pairs,

On cycleβ€”Complete graph ramsey numbers
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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

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## Abstract Let __r(k__) denote the least integer __n__‐such 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: _