Fig. 11

From a digraph \(G\) for \(LPSTP\) to a digraph \(G'\) for \(\mathcal {IRP}\). Bold red edges in both sub-figures correspond to the solution path for \(LPSTP\) and \(\mathcal {IRP}\) problems, respectively. a \(G_{V {\setminus } \{s,t\}}\) is the subgraph induced by the vertex set \(V {\setminus } \{s,t\}\). As the longest path exits \(s\) and enters \(t\), dashed edges do not participate in the solution. b Green dashed line between vertices in \(G'_{f0}\) and \(G'_{r1}\) visualise the inverted fragments