Algorithms for the independent feedback vertex set problem

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9 Citations (Scopus)


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 languageEnglish
Pages (from-to)1179-1188
Number of pages10
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number6
Publication statusPublished - 2015 Jun 1


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


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