The Ramsey numbers of wheels versus odd cycles
β 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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π SIMILAR VOLUMES
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
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
## 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 twoβcoloring of the edges of the complete 5βpartite graph __K__((__n__β1)/2, (__n__β1)/2, (__n__β1)/2, (__n__β1)/2, 1)