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categories: Graph theory
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## In directed acyclic graphs
Path cover in a [directed acyclic graph](Directed acyclic graph) can be reduced to [vertex-disjoint path cover](Vertex-disjoint path cover) in a directed acyclic graph by first taking the [transitive closure](Transitive closure).

> **Insight**: If a directed acyclic graph is transitive (i.e. is its own transitive closure), as is the case for [partially ordered sets](Partially ordered set), then the path cover problem is equivalent to the vertex-disjoint path 
cover problem.

## Problems
- [Skiers](http://main.edu.pl/en/archive/oi/9/nar)

## See also
- [Vertex-disjoint path cover]()
- [Dilworth's theorem](Dilworth's theorem)