A theorem on cycle–wheel Ramsey number

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 . In this paper, we show that R ( C n , W m ) = 3 n − 2 for m odd, n ≥ m ≥ 3 and ( n , m ) ≠ ( 3 , 3 ) , which was conjectured by Surahmat, Baskoro and Tomescu.