The Ramsey numbers of wheels versus odd cycles

Given two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that for any graph G of order N, either G contains G1 or its complement contains G2. Let Cm denote a cycle of order m and Wn a wheel of order n+1. In this paper, it is shown that R(Wn,Cm)=2n+1 for m odd, n≥3(m−1)/2 and (m,n)≠(3,3),(3,4), and R(Wn,Cm)=3m−2 for m,n odd and m