The minimum-degree wheel conjecture

Let $W_{2k}$ be the wheel on $2k+1$ vertices, let $G$ be a graph on $n$ vertices, and let $\delta(G)$ denote its minimum degree. Minimum-degree wheel conjecture. For all integers $n$ and $k$ with $3\leq k<\frac{n}{3}$, if

$$\delta(G)\geq \begin{cases} \left\lfloor\frac{n+k}{2}\right\rfloor, & \text{$k-1$ is odd and $\left\lfloor\frac{n+k}{2}\right\rfloor$ is odd},\\ \left\lceil\frac{n+k}{2}\right\rceil, & \text{otherwise}, \end{cases}$$

then $W_{2k}\subseteq G$; furthermore, this degree condition is best possible. This is presented as an equivalent formulation of the star–wheel conjecture and would extend the paper’s exact minimum-degree results to the full range $3\leq k<\frac n3$.