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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References

Publications referenced by this paper.
Showing 1-10 of 33 references

On enumerating all minimal solutions of feedback problems

Discrete Applied Mathematics • 2002
View 5 Excerpts
Highly Influenced

On Cliques in Graphs

View 4 Excerpts
Highly Influenced

Directed Feedback Vertex Set Problem is FPT

Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs • 2007
View 1 Excerpt

Directed Feedback Vertex Set is Fixed-Parameter Tractable

Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs • 2007
View 1 Excerpt

An O*(2^n ) Algorithm for Graph Coloring and Other Partitioning Problems via Inclusion--Exclusion

2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) • 2006
View 1 Excerpt

Inclusion--Exclusion Algorithms for Counting Set Partitions

2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) • 2006

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