The Ramsey Number for Tree Versus Wheel with Odd Order

Chen et al. (Appl Math Lett 17:281–285, 2004) conjectured that for even m, $$R(T_n,W_m)=2n-1$$ if the maximum degree $$\varDelta (T_n)$$ is small. However, they did not state how small it is. Related to this conjecture, also interesting know which tree $$T_n$$ causes Ramsey number $$R(T_n,W_m)$$ be greater than $$2n-1$$ whenever m even. In paper, we determine $$R(T_n,W_8)$$ all trees with (T_n) \ge n-3$$ . For most cases of these trees, $$R(T_n,W_8) > 2n-1$$ Furthermore, prove certain values n, and Finally, refine above conjecture by giving an upper bound on