Ramsey Numbers of a Wheel of Order Five Versus Fans

For graphs G and H, the Ramsey number r(G, H) is the smallest number N, such that any red/blue edge-coloring of KN contains either a red copy of G or a blue copy of H. Let Fn = K1 + nK2 be a fan and W4 = K1 + C4 be a wheel of order five. In this paper, we show that the Ramsey number r(W4, Fn) = 4n + 1 for all sufficiently large n. Moreover, this implies that a large fan Fn is W4-good.