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The Ramsey numbers of wheels versus odd cycles

✍ Scribed by Zhang, Yanbo; Zhang, Yunqing; Chen, Yaojun


Book ID
123196404
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
371 KB
Volume
323
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES


The Ramsey numbers for cycles versus whe
✍ Yaojun Chen; T.C. Edwin Cheng; Zhengke Miao; C.T. Ng πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 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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We prove that the chromatic Ramsey number of every odd wheel W 2k+1 , k β‰₯ 2 is 14. That is, for every odd wheel W 2k+1 , there exists a 14-chromatic graph F such that when the edges of F are two-coloured, there is a monochromatic copy of W 2k+1 in F, and no graph F with chromatic number 13 has the s

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

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3-colored Ramsey Numbers of Odd Cycles
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