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Recently, the authors gave Ramsey-type results for the path cover/partitionnumber of graphs. In this paper, we continue the research about them focusingon digraphs, and find a relationship between the path cover/partition numberand forbidden structures in digraphs.  Let $D$ be a weakly connected digraph. A family $\mathcal{P}$ of subdigraphsof $D$ is called a {\it path cover} (resp. a {\it path partition}) of $D$ if$\bigcup _{P\in \mathcal{P}}V(P)=V(D)$ (resp. $\dot\bigcup _{P\in\mathcal{P}}V(P)=V(D)$) and every element of $\mathcal{P}$ is a directed path.The minimum cardinality of a path cover (resp. a path partition) of $D$ isdenoted by ${\rm pc}(D)$ (resp. ${\rm pp}(D)$). In this paper, we findforbidden structure conditions assuring us that ${\rm pc}(D)$ (or ${\rmpp}(D)$) is bounded by a constant.

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