Star-Critical Ramsey Numbers of Cycles Versus Wheels

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 Kr-1 coproduct K-1,K-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 Kr-1 coproduct K-1,K-k is the graph obtained from a Kr-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 >= 5. In this paper, it is shown that r(*)(C-n,W-m) = 2n for m odd, n >= m >= 5 and n >= 60.