The Ramsey numbers for cycles versus wheels of odd order

For two given graphs G(1) and G(2), the Ramsey number R(G(1), G(2)) is the smallest integer n Such chat 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. in) 0 (4, 4). In this paper, we confirm the conjecture for n >= 3m/2 + 1. (C) 2009 Elsevier Ltd. All rights reserved.