Recall the following branching algorithm for Feedback Vertex Set (FVS) discussed in class:

- Preprocess to eliminate vertices of degree at most two, resulting in an equivlaent multigraph.
- Preprocess to force vertices with self-loops in the solution and adjust the budget as appropriate.
- If a pair of vertices have more than two edges between them, delete all but two of these edges.
- STOP if the graph is a forest or if we are out of budget.
- Find a shortest cycle and branch on all its vertices.

Since a graph of minimum degree three that is not acyclic always has a cycle of length O(\lg n), this algorithm has a running time of O^\star((\lg n)^k). Argue that this running time in fact shows that FVS is FPT in k.