The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph $$W_8$$

Abstract

The Ramsey numbers \(R(T_n,W_8)\) are determined for each tree graph \(T_n\) of order \(n\ge 7\) and maximum degree \(\Delta (T_n)\) equal to either \(n-4\) or \(n-5\). These numbers indicate strong support for the conjecture, due to Chen, Zhang and Zhang and to Hafidh and Baskoro, that \(R(T_n,W_m) = 2n-1\) for each tree graph \(T_n\) of order \(n\ge m-1\) with \(\Delta (T_n)\le n-m+2\) when \(m\ge 4\) is even.