Computing subset transversals in H-free graphs

We study the computational complexity of two well-known graph transversal problems, namely Subset Feedback Vertex Set and Subset Odd Cycle Transversal, by restricting the input to H-free graphs, that is, to graphs that do not contain some fixed graph H as an induced subgraph. By combining known and...

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Bibliographic Details
Published in:Theoretical computer science 2022-01, Vol.902, p.76-92
Main Authors: Brettell, Nick, Johnson, Matthew, Paesani, Giacomo, Paulusma, Daniël
Format: Article
Language:English
Subjects:
Complexity dichotomy
Feedback vertex
H-free
Hereditary graph class
Odd cycle transversal
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Summary:We study the computational complexity of two well-known graph transversal problems, namely Subset Feedback Vertex Set and Subset Odd Cycle Transversal, by restricting the input to H-free graphs, that is, to graphs that do not contain some fixed graph H as an induced subgraph. By combining known and new results, we determine the computational complexity of both problems on H-free graphs for every graph H except when H=sP1+P4 for some s≥1. As part of our approach, we introduce the Subset Vertex Cover problem and prove that it is polynomial-time solvable for (sP1+P4)-free graphs for every s≥1.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2021.12.010