The skew Loebl–Komlós–Sós conjecture

Let a $k$-edge tree be $r$-skew if one of its colour classes has size at most $r(k+1)$. Skew Loebl–Komlós–Sós conjecture. If a graph $G$ on $n$ vertices has more than $rn$ vertices of degree at least $k$, then $G$ contains every $r$-skew $k$-edge tree. The source records approximate results for large dense graphs and verification for paths and trees of diameter at most five, but leaves the general conjecture open.