eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-08-18
82:1
82:14
10.4230/LIPIcs.MFCS.2021.82
article
Feedback Vertex Set and Even Cycle Transversal for H-Free Graphs: Finding Large Block Graphs
Paesani, Giacomo
1
https://orcid.org/0000-0002-2383-1339
Paulusma, Daniël
1
https://orcid.org/0000-0001-5945-9287
Rzążewski, Paweł
2
3
https://orcid.org/0000-0001-7696-3848
Department of Computer Science, Durham University, UK
Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland
Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Poland
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol202-mfcs2021/LIPIcs.MFCS.2021.82/LIPIcs.MFCS.2021.82.pdf
Feedback vertex set
even cycle transversal
odd cactus
forest
block