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

Recently, the authors [Electron. J. Combin. 29 (2022), Paper No. 4.8] 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 P of subdigraphs of D is called a path cover (resp. a path partition ) of D if U � P & ISIN; P V (P) = V (D ) (resp. P & ISIN; PV (P) = V(D)) and every element of P is a directed path. The minimum cardinality of a path cover (resp. a path partition) of D is denoted by pc(D) (resp. pp(D)). In this paper, we find forbidden structure conditions assuring us that pc(D) (or pp(D)) is bounded by a constant. & COPY; 2023 Elsevier Inc. All rights reserved.