Ramsey numbers of trees versus fans

For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integerN such that, for any graph G of order N, either G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. Let Tn be a tree of order n, Sn a star of order n, and Fm a fan of order 2m + 1, i.e., m triangles sharing exactly one vertex. In this paper, we prove that R(Tn, Fm) = 2n − 1 for n ≥ 3m^2 − 2m − 1, and if Tn = Sn, then the range can be replaced by n ≥ max m(m−1)+1,6(m−1), which is tight in some sense