 consists of finitely many line segments $c_0, \dots, c_k$, $k >0$, whose endpoints are vertices of ${\mathcal{T}}$, $c=  c_0 \dots c_k$, and $c$ is closed. If $c_i \subset {\mathcal{T}}$ then the ${\mathcal{T}}$-length $|c_i|_{{\mathcal{T}}}$ of $c_i$ is the number of edges of $