## 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.

Original language | English |
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Pages (from-to) | 1179-1188 |

Number of pages | 10 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E98A |

Issue number | 6 |

DOIs | |

Publication status | Published - 2015 Jun 1 |

## Keywords

- Fixed parameter tractability
- Graph algorithm
- Independent feedback vertex set

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics