Definition
The decision problem is as follows:
- INSTANCE: An (undirected or directed) graph and a positive integer .
- QUESTION: Is there a subset with such that with the vertices from deleted is cycle-free?
The graph that remains after removing from is an induced forest (resp. an induced directed acyclic graph in the case of directed graphs). Thus, finding a minimum feedback vertex set in a graph is equivalent to finding a maximum induced forest (resp. maximum induced directed acyclic graph in the case of directed graphs).
Read more about this topic: Feedback Vertex Set
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