The sharp Loebl–Komlós–Sós conjecture

Let $G$ be an $n$-vertex graph, and let $k$ be a positive integer. Sharp Loebl–Komlós–Sós conjecture. If more than $\frac n2-\left\lfloor\frac{n}{k+1}\right\rfloor-(n\mathbin{\bmod}(k+1))$ vertices of $G$ have degree at least $k$, then $G$ contains every tree with $k$ edges. This refines the proposed $n/2$ threshold using the extremal examples described in the survey. Its resolution is not supplied in the source.