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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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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


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

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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)


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
  • Feedback vertex set
  • even cycle transversal
  • odd cactus
  • forest
  • block


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