Li–Wu's lower-bound conjecture for conflict-free connection numbers of trees

Let $T$ be a tree of order $n$, and let $P_n$ be the path on $n$ vertices. Write $cfc(G)$ for the conflict-free connection number of a graph $G$. Li–Wu's conjecture. For every tree $T$ of order $n$,

$$cfc(T)\geq cfc(P_n)=\lceil\log_{2} n\rceil.$$

The conjecture asserts that among trees of a fixed order, the path minimizes the conflict-free connection number. The surrounding results determine this number for paths and several other tree classes, but the general lower bound is presented as a conjecture.