Fig. 3

A 2-break \(\{a,b\},\{d,c\}\rightarrow \{a,d\},\{b,c\}\) transforming a graph G into a terminal one is depicted on the left. A directed graph \(\mathcal {D} (G,\rho )\) is obtained from \(\mathcal {D} (G,\rho _{0})\) on the right for this scenario \(\rho\) of length 1. The endpoints of the edges labeled \(\{a,b\}\) and \(\{d,c\}\) are merged and two new edges labeled \(\{a,d\}\) and \(\{b,c\}\) are introduced. \(\mathcal {D} (G,\rho )\) has 2 connected components that correspond to the 2 simple cycles of G.