LAUSR

For two graphs $$G_1$$ and $$G_2$$ , the star-critical Ramsey number $$r_*(G_1,G_2)$$ is the minimum integer k such that any red/blue edge-coloring of $$K_{r-1}\sqcup K_{1,k}$$ contains a red copy of $$G_1$$ or a blue copy of $$G_2$$ , where r is the classical Ramsey number $$R(G_1,G_2)$$ and $$K_{r-1}\sqcup K_{1,k}$$ is the graph obtained from a $$K_{r-1}$$ and an additional vertex v by joining v to k vertices of $$K_{r-1}$$ . Let $$C_n$$ denote a cycle of order n and $$W_m$$ a wheel of order $$m+1$$ . Hook (2010) proved that $$r_*(C_n,W_3)=2n$$ for $$n\ge 5$$ . In this paper, it is shown that $$r_*(C_n,W_m)=2n$$ for m odd, $$n\ge m\ge 5$$ and $$n\ge 60$$ .