Let $H=(V_H,A_H)$ be a digraph, possibly with loops, and let $D=(V_D, A_D)$ loopless multidigraph colouring of its arcs $c: A_D \rightarrow V_H$. An $H$-path $D$ is path $(v_0, \dots, v_n)$ such that $(c(v_{i-1}, v_i), c(v_i,v_{i+1}))$ an arc $H$ for every $1 \le i n-1$. For $u, v \in V_D$, we say $u$ reaches $v$ by $H$-paths if there exists from to in $D$. A subset $S \subseteq V_D$ $H$-absorb...