Feedback Vertex Set and Even Cycle Transversal for H-Free Graphs: Finding Large Block Graphs
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.
Feedback vertex set
even cycle transversal
odd cactus
forest
block
Mathematics of computing~Graph algorithms
82:1-82:14
Regular Paper
https://arxiv.org/abs/2105.02736
The first author thanks Carl Feghali for an inspiring initial discussion.
Giacomo
Paesani
Giacomo Paesani
Department of Computer Science, Durham University, UK
https://orcid.org/0000-0002-2383-1339
Daniël
Paulusma
Daniël Paulusma
Department of Computer Science, Durham University, UK
https://orcid.org/0000-0001-5945-9287
Supported by the Leverhulme Trust (RPG-2016-258).
Paweł
Rzążewski
Paweł Rzążewski
Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland
Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Poland
https://orcid.org/0000-0001-7696-3848
Supported by Polish National Science Centre grant no. 2018/31/D/ST6/00062.
10.4230/LIPIcs.MFCS.2021.82
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Giacomo Paesani, Daniël Paulusma, and Paweł Rzążewski
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