Ramsey-type results for path covers and path partitions. II. digraphs

•Let Γ be (di)graph. A family P of sub(di)graphs of Γ is called a path cover (resp. a path partition) of Γ if ∪pϵPV(P)=V(Γ) (resp. ∪pϵPV(P)=V(Γ)) and every element of P is a path or a directed path. The minimum cardinality of a path cover (resp. a path partition) of Γ is denoted by pc(Γ) (resp. pp(Γ)).•The authors recently gave Ramsey-type results for the path cover/partition number of graphs.•We continue the research about them focusing on digraphs, and find a relationship between the path cover/partition number and forbidden structures in digraphs.•In this paper, we find forbidden structure conditions assuring us that pc(D) (or pp(D)) is bounded by a constant for every weakly connected digraph D.