... with directed graphs,they stated the PPC only for undirected graphs. In 1995 Bondy [2] stated a directedversion of the PPC. In [3] the PPC is stated in the language of the theory of hereditaryproperties ... ,Hkbe the components of H. Then the following hold:(a) If u ∈ V (P ) , then NHi(u) ∩ NHi(u+)=∅, for i =1, ,k.(b) If {u, v}⊆NP(Hi) for some i, then {u+,v+}⊆NP(Hj) for any ... (wk)| =1,then NI(wk) ⊆ NI(wi) ∩ N (wj) for all k such that i ≤ k ≤ j.(4) If I ⊆ V [ws,w−s+1] for some s ∈{1, ,r− 1}, then the I-neighbourhoods of the vertices in W appear in the order...