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The Ramsey Numbers of Large cycles Versus Odd Wheels

✍ Scribed by Surahmat; E. T. Baskoro; Ioan Tomescu


Publisher
Springer Japan
Year
2008
Tongue
English
Weight
87 KB
Volume
24
Category
Article
ISSN
0911-0119

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πŸ“œ SIMILAR VOLUMES


The Ramsey numbers for cycles versus whe
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For two given graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2 ) is the smallest integer n such that for any graph G of order n, either G contains G 1 or the complement of G contains G 2 . Let C n denote a cycle of order n and W m a wheel of order m + 1. It is conjectured by Surahmat, E.T. Baskoro

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## Abstract Let __r__~__k__~(__G__) be the __k__‐color Ramsey number of a graph __G__. It is shown that $r\_{k}(C\_{5})\le \sqrt{18^{k}\,k!}$ for __k__β©Ύ2 and that __r__~__k__~(__C__~2__m__+ 1~)β©½(__c__^__k__^__k__!)^1/__m__^ if the Ramsey graphs of __r__~__k__~(__C__~2__m__+ 1~) are not far away fr

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Chvatal established that r(T,, K,,) = (m -1 ) ( n -1 ) + 1, where T, , , is an arbitrary tree of order m and K, is the complete graph of order n. This result was extended by Chartrand, Gould, and Polimeni who showed K, could be replaced by a graph with clique number n and order n + 5 provided n 2 3