4 problems

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…

Let $T$ be a tree of order $n$, and let $cfc(T)$ denote its conflict-free connection number, the smallest number of edge colors needed so that every two vertices are joined by a pa…

Let $G$ be a connected graph of order $n$. The conflict-free vertex-connection number $vcfc(G)$ is the smallest number of colors required for a vertex-coloring in which every two v…

Let $G$ be a connected graph of order $n$. The path extremal conjecture. … Here $vcfc(G)$ denotes the conflict-free vertex-connection number of $G$, and $P_n$ is the path on $n$ ve…