The Ramsey numbers of large trees versus wheels

For two given 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 the complement of G contains G2. Let Tn denote a tree of order n and Wm a wheel of order m+1. To the best of our knowledge, only R(Tn,Wm) with small wheels are known. In this paper, we show that R(Tn,Wm)=3n−2 for odd m with n 756m^10.