Covering Edges in DAG

117 Views Asked by At

On my textbook a covering edge is defined as:

if a and b are distinct vertices of a digraph, then a is said to cover b if there is an edge from a to b and every path from a to b traverses this edge. If a covers b, the edge from a to b is called a covering edge.

And I'm working on the problem to prove:

If there is a path in DAG D from a vertex, u, to vertex, v, then there is a path from u to v that only traverses covering edges

I think and I looked up online, DAG should only require no directed cycle (as opposed to cycle), so if we have something like this with a->b->d, a->c->d, then wouldn't a to d doesn't have covering edges?

Thank you.

(Problem source: problem 2)