The sparse minimum/maximum degree conjecture for tree containment

Let $G$ be an $n$-vertex graph, and let $k$ be a positive integer. Sparse degree conjecture. If $\delta(G)\ge\frac k2$ and at least $\frac{n}{2\sqrt{k}}$ vertices of $G$ have degree at least $k$, then $G$ contains every tree with $k$ edges. The conjecture combines the skew Loebl–Komlós–Sós perspective with minimum-degree conditions. The source presents it as new and open.