Fig. 4

Example for unsatisfiable relations \(U(\vec {G},{\mathcal {V}})\) of a vertex-colored digraph \((\vec {G}=(V,E),\sigma )\) w.r.t. a partition \({\mathcal {V}}=\{V_1,V_2\}\) (indicated by the gray boxes). In the middle, the set of trees \({\mathcal {T}}({\mathcal {V}})\) is illustrated, i.e., the triangles represent all possible phylogenetic trees on the respective subset of leaves. On the right, the arc modifications implied by \({\mathcal {V}}\) (i.e., \(U(\vec {G},{\mathcal {V}})\)) are illustrated where \(U_1\), \(U_2\), and \(U_3\) indicate the type according to Lemma 13