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Feedback Vertex Set and Even Cycle Transversal for H-Free Graphs: Finding Large Block Graphs

Authors Giacomo Paesani , Daniël Paulusma , Paweł Rzążewski

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Author Details

Giacomo Paesani
  • Department of Computer Science, Durham University, UK
Daniël Paulusma
  • Department of Computer Science, Durham University, UK
Paweł Rzążewski
  • Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland
  • Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Poland

Funding

  • Paulusma, Daniël: Supported by the Leverhulme Trust (RPG-2016-258).
  • Rzążewski, Paweł: Supported by Polish National Science Centre grant no. 2018/31/D/ST6/00062.

Acknowledgements

The first author thanks Carl Feghali for an inspiring initial discussion.

Cite As Get BibTex

Giacomo Paesani, Daniël Paulusma, and Paweł Rzążewski. Feedback Vertex Set and Even Cycle Transversal for H-Free Graphs: Finding Large Block Graphs. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 82:1-82:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.MFCS.2021.82

Abstract

We prove new complexity results for Feedback Vertex Set and Even Cycle Transversal on H-free graphs, that is, graphs that do not contain some fixed graph H as an induced subgraph. In particular, we prove that both problems are polynomial-time solvable for sP₃-free graphs for every integer s ≥ 1; here, the graph sP₃ denotes the disjoint union of s paths on three vertices. Our results show that both problems exhibit the same behaviour on H-free graphs (subject to some open cases). This is in part explained by a new general algorithm we design for finding in a graph G a largest induced subgraph whose blocks belong to some finite class C of graphs. We also compare our results with the state-of-the-art results for the Odd Cycle Transversal problem, which is known to behave differently on H-free graphs.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • Feedback vertex set
  • even cycle transversal
  • odd cactus
  • forest
  • block

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References

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