Fig. 6.

The 3-RBMG $(G,\sigma )$ is explained by two trees $(T_1,\sigma )$ and $(T_2,\sigma )$. These induce distinct BMGs $\overrightarrow{G}(T_1,\sigma )$ and $\overrightarrow{G}(T_2,\sigma )$. In $\overrightarrow{G}(T_1,\sigma )$, $P^1=⟨a_1{b}_1{c}_1{a}_2⟩$ defines a good quartet, while $P^2=⟨a_1{c}_2{b}_2{a}_2⟩$ induces a bad quartet. In $\overrightarrow{G}(T_2,\sigma )$ the situation is reversed. The good quartets in $\overrightarrow{G}(T_1,\sigma )$ and $\overrightarrow{G}(T_2,\sigma )$ are indicated by red edges. The induced paths $⟨a_1{b}_1{c}_1{b}_2⟩$ and $⟨a_2{c}_1{b}_1{c}_2⟩$ are examples of ugly quartets. Figure reused from (Geiß et al. 2019b), ©Springer (color figure online)