Question

Give a counterexample to the conjecture that if a directed graph G contains a path from u to , then any depth-first search must result in v.d ≤ u.f.

Solution

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An idea would be to end a branch of a graph with uu and then go back to vv. That would give us v.d>u.fv.d>u.f, which is what we have to show.
[7pt]

We need not look any further for a counterexample, in fact, we only need to look back to a previous problem where we had the following search:

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