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 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 ) = 2 n − 1 for even m ≥ 4 , n ≥ m and ( n , m ) ≠ ( 4 , 4 ) . In this paper, we confirm the conjecture for n ≥ 3 m / 2 + 1 .