Figure 10:

Left panel: A forest $ℱ$ (in this example just a tree) with root $r$ and node $v$. Right panel: Tree $T(v)$ and forest $R(ℱ,v)$ obtained from $ℱ$ by deleting all nodes on the path from $r$ to $v$ and adding to $ℱ$ the subtrees of any children node $c\notin P(r,v)$ whose parent $p\in P(r,v)\backslash \left\{v\right\}$ has been deleted.