Li–Schiermeyer’s star–wheel Ramsey conjecture

Let $R(G,H)$ denote the Ramsey number of graphs $G$ and $H$, let $K_{1,m}$ be the star with $m$ leaves, and let $W_{2n}$ be the wheel on $2n+1$ vertices. Li–Schiermeyer’s conjecture. Their formula

$$R(K_{1,m}, W_{2n})= \begin{cases} 2m+n-1, & m \text{ and } n \text{ are even},\\ 2m+n, & \text{otherwise} \end{cases}$$

should hold for all integers $m\geq 2n-1\geq 4$. The conjecture would determine the exact star–wheel Ramsey number in the remaining range beyond the results established in the paper.