\begin{definition}[Definition:Rooted Tree/Branch]
Let $T$ be a rooted tree with root node $r_T$.
A subset $\Gamma$ of $T$ is a '''branch''' {{iff}} all the following conditions hold:
:$(1): \quad$ The root node $r_T$ belongs to $\Gamma$
:$(2): \quad$ The parent of each node in $\Gamma \setminus \left\{{r_T}\right\}$ is in $\Gamma$
:$(3): \quad$ Each node in $\Gamma$ either:
::$(a): \quad$ is a leaf node of $T$
:or:
::$(b): \quad$ has exactly one child node in $\Gamma$.
Informally, a '''branch''' of a rooted tree is the path from the root to a leaf.
\end{definition}