can be grouped into bunches of leaves in an unique way.

![*In this example, the leaf $(v,w)$ is removed, as well as the four edges touching $v$: the new graph $G'$ is the subgraph of $G$ induced by the five remaining vertices. Note that the vertex $t$ is now isolated, and that a new leaf $(z,y)$ has been created.*[]{data-label="fig:eff"}](eff.eps){width="\figwidth" height="0.9\textheight"}

**Leaf removal**: If $(v,w)$ is a leaf of $G$, and $G'$ the subgraph of $G$ induced by $V \backslash \{v,w\}$, we say that $G'$ is obtained from $G$ by leaf removal of $(v,w)$. In other words, $G'$ is obtained from $G$ by removing vertices $v$ and $w$, the edge $\{v,w\}$ and all other edges touching $v$. Note that this operation can destroy other leaves of $G$ and also create new leaves. See Fig. \[fig:eff\] for a pictorial example.

**Step by step leaf removal process**: Start from a graph $G$. If $G$ has no leaves, stop. Else, choose a leaf $(v,w)$ and remove it, leading to a graph $G'$. If $G'$ has no leaves, stop. Else, choose a leaf $(v',w')$ and remove it. This operation is iterated until no leaf remains.

**History**: A sequence $G,(v,w),G',(v',w'),\cdots$ associated to a step by step 