International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 351-363

# Deterministic Algorithms for the Independent Feedback Vertex Set Problem

• Yuma Tamura
• Takehiro Ito
• Xiao Zhou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)

## Abstract

A feedback vertex set F of an undirected graph G is a vertex subset of G whose removal results in a forest. Such a set F is said to be independent if F forms an independent set of G. In this paper, we study the problem of finding an independent feedback vertex set of a given graph with the minimum number of vertices, from the viewpoint of graph classes. This problem is NP-hard even for planar bipartite graphs of maximum degree four. However, we show that the problem is solvable in linear time for graphs having tree-like structures, more specifically, for bounded treewidth graphs, chordal graphs and cographs. We then give a fixed-parameter algorithm for planar graphs when parameterized by the solution size. Such a fixed-parameter algorithm is already known for general graphs, but our algorithm is exponentially faster than the known one.

## Notes

### Acknowledgments

We are grateful to Saket Saurabh for fruitful discussions with him. This work is partially supported by JSPS KAKENHI Grant Numbers 25106504 and 25330003.

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