# On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms

@article{Fomin2007OnTM,
title={On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms},
author={Fedor V. Fomin and Serge Gaspers and Artem V. Pyatkin and Igor Razgon},
journal={Algorithmica},
year={2007},
volume={52},
pages={293-307}
}
We present a time $\mathcal {O}(1.7548^{n})$ algorithm finding a minimum feedback vertex set in an undirected graph on n vertices. We also prove that a graph on n vertices can contain at most 1.8638 n minimal feedback vertex sets and that there exist graphs having 105 n/10≈1.5926 n minimal feedback vertex sets.

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