# A note on the complexity of Feedback Vertex Set parameterized by mim-width

@article{Jaffke2017ANO, title={A note on the complexity of Feedback Vertex Set parameterized by mim-width}, author={Lars Jaffke and O-joung Kwon and Jan Arne Telle}, journal={ArXiv}, year={2017}, volume={abs/1711.05157} }

We complement the recent algorithmic result that Feedback Vertex Set is XP-time solvable parameterized by the mim-width of a given branch decomposition of the input graph [3] by showing that the problem is W[1]-hard in this parameterization. The hardness holds even for linear mim-width, as well as for H-graphs, where the parameter is the number of edges in H. To obtain this result, we adapt a reduction due to Fomin, Golovach and Raymond [2], following the same line of reasoning but adding a new… CONTINUE READING

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#### Citations

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## Matrix decompositions and algorithmic applications to (hyper)graphs. (Décomposition de matrices et applications algorithmiques aux (hyper)graphes)

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## On the Tractability of Optimization Problems on H-Graphs

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## Mim-Width II. The Feedback Vertex Set Problem

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## Subset Feedback Vertex Set on Graphs of Bounded Independent Set Size

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## On the tractability of optimization problems on H-graphs

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