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A multipartite Ramsey number for odd cycles

✍ Scribed by Fabrıcio Siqueira Benevides

Book ID
115558794
Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
272 KB
Volume
71
Category
Article
ISSN
0364-9024

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📜 SIMILAR VOLUMES

Multipartite Ramsey numbers for odd cycl
Multipartite Ramsey numbers for odd cycles
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## Abstract In this paper we study multipartite Ramsey numbers for odd cycles. We formulate the following conjecture: Let __n__≥5 be an arbitrary positive odd integer; then, in any two‐coloring of the edges of the complete 5‐partite graph __K__((__n__−1)/2, (__n__−1)/2, (__n__−1)/2, (__n__−1)/2, 1)

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✍ Yaojun Chen; T.C. Edwin Cheng; Zhengke Miao; C.T. Ng 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 267 KB

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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✍ Yusheng Li 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 73 KB

## 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__⩾2 and that __r__~__k__~(__C__~2__m__+ 1~)⩽(__c__^__k__^__k__!)^1/__m__^ if the Ramsey graphs of __r__~__k__~(__C__~2__m__+ 1~) are not far away fr