The Ramsey numbers for cycles versus wheels of even 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 . Surahmat, Baskoro and Tomescu conjectured that R ( C n , W m ) = 3 n − 2 for m odd, n ≥ m ≥ 3 and ( n , m ) ≠ ( 3 , 3 ) . In this paper, we confirm the conjecture for n ≥ 20 .