English

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

Computational Complexity 2017-11-15 v1 Data Structures and Algorithms

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.

Keywords

Cite

@article{arxiv.1711.05157,
  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 preprint arXiv:1711.05157},
  year   = {2017}
}

Comments

7 pages, 3 figures

R2 v1 2026-06-22T22:45:41.804Z