Klimošová–Piguet–Rohzoň skew-tree conjecture

Let $r$ be a parameter, let $G$ be an $n$-vertex graph, and call a tree $T$ $r$-skew if one of its parts has order at most $r|T|$.

Klimošová–Piguet–Rohzoň conjecture. If at least $rn$ vertices of $G$ have degree at least $d$, then $G$ contains a copy of every $r$-skew tree with $d$ edges.

This sharpens the Loebl–Komlós–Sós conjecture by incorporating the bipartite skew of the target tree. It is listed among the related unsolved bounded-degree problems.