Komlós–Sós conjecture on degree-sequence conditions for tree embeddings

Let $G$ be a graph on $n$ vertices, and let $k$ be a positive integer. A tree with $k$ edges has $k+1$ vertices. Komlós–Sós conjecture. If at least $n/2$ vertices of $G$ have degree at least $k$, then $G$ contains every tree with $k$ edges. This conjecture is presented as a generalization of a theorem of Zhao and is part of the effort to characterize degree conditions forcing tree embeddings; the source does not report a resolution.