The Ramsey numbers R(Tn, W6) for Δ(Tn) ≥ n−3 Original Research Article

Let Tn denote a tree of order n and Wm a wheel of order m + 1. In a previous paper, we evaluated the Ramsey number R(Tn, Wm) in the cases where Tn is the star of order n and m = 6 or m is odd and n ≥ m − 1 ≥ 2. In this paper, we determine R(Tn, W6) in the case where the maximum degree of Tn is at least n − 3. Our results show that a recent conjecture of Baskoro et al. is false.