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

Lars Jaffke; O-joung Kwon; Jan Arne Telle

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arXiv · 1711.05157

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

Lars Jaffke·O-joung Kwon·Jan Arne Telle

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Abstract

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 gadget.

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Lars Jaffke, O-joung Kwon, Jan Arne Telle. 2017-11-14. A note on the complexity of Feedback Vertex Set parameterized by mim-width. https://arxiv.org/abs/1711.05157

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