The Burning Graph Conjecture for trees

Let $T$ be a tree on $n$ vertices. For a set $B\subseteq\mathbb{N}$, say that $T$ is $B$-burnable if there is a sequence of vertices $X=\{v_1,\ldots,v_j\}$ such that

$$\bigcup_{i\in\{1,\ldots,j\}}N_{b_i}[v_i]=V(T),$$

where $B=\{b_1,\ldots,b_j\}$. Here $N_r[v]$ denotes the closed radius-$r$ neighborhood of $v$.

Burning Graph Conjecture. Every tree $T$ on $n$ vertices is $\{0,\ldots,\lceil\sqrt{n}\rceil-1\}$-burnable.

This is the tree formulation of the general burning conjecture. It remains open in general, while the paper proves reductions for trees of bounded growth and establishes improved approximate bounds.