Klimošová–Piguet–Rozhoň local degree conjecture

Let $G$ be a graph, and let $d$ be a nonnegative integer.

Klimošová–Piguet–Rozhoň local degree conjecture. If

$$\delta(G)\geq d/2$$

and at least $|G|/(2\sqrt d)$ vertices of $G$ have degree $d$, then $G$ contains a copy of every tree with $d$ edges.

This is a local degree variant of the Erdős–Sós problem. It is listed among the related unsolved problems, with the source indicating only forthcoming progress for such degree conditions.