Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramsey-type results for path covers and path partitions. II. Digraphs   Recently, the authors gave Ramsey-type results for the path cover/partition
number of graphs. In this paper, we continue the research about them focusing
on digraphs, and find a relationship between the path cover/partition number
and forbidden structures in digraphs.
  Let $D$ be a weakly connected digraph. A family $\mathcal{P}$ of subdigraphs
of $D$ 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 $D$ is
denoted by ${\rm pc}(D)$ (resp. ${\rm pp}(D)$). In this paper, we find
forbidden structure conditions assuring us that ${\rm pc}(D)$ (or ${\rm
pp}(D)$) is bounded by a constant.

25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph