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The Ramsey numbers for cycles versus wheels of odd order

✍ Scribed by Yaojun Chen; T.C. Edwin Cheng; Zhengke Miao; C.T. Ng

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 267 KB
Volume: 22
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2009.07.014

No coin nor oath required. For personal study only.

✦ Synopsis

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 and I. Tomescu that R(C n , W m ) = 2n -1 for even m ≥ 4, n ≥ m and (n, m) = (4, 4). In this paper, we confirm the conjecture for n ≥ 3m/2 + 1.

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