 $c_i$. If $c_i \not\subset {\mathcal{T}}$ then the ${\mathcal{T}}$-length $|c_i|_{{\mathcal{T}}}$ of $c_i$ is the number of connected components in $c_i  \setminus {\mathcal{T}}$. We assume that $|c_i|_{{\mathcal{T}}} >0$ for every $i$ and set $|c|_{{\mathcal{T}}} := \sum_{i=0}^k |c_i|_{{\mathcal{T}}}$.  