The $2k$–$k/2$ degree conjecture

Let $G$ be a graph, and let $k$ be a positive integer. $2k$–$k/2$ conjecture. If $\delta(G)\ge\frac{k}{2}$ and $\Delta(G)\ge2k$, then $G$ contains every tree with $k$ edges. This is a companion minimum/maximum-degree condition to the two-thirds conjecture. The source reports only approximate and bounded-maximum-degree results, so the full statement remains open.