Classifying subset feedback vertex set for H-free graphs

In the Feedback Vertex Set problem, we aim to find a small set S of vertices in a graph intersecting every cycle. The Subset Feedback Vertex Set problem requires S to intersect only those cycles that include a vertex of some specified set T. We also consider the Weighted Subset Feedback Vertex Set p...

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Bibliographic Details
Published in:Theoretical computer science 2024-07, Vol.1003, p.114624, Article 114624
Main Authors: Paesani, Giacomo, Paulusma, Daniël, Rzążewski, Paweł
Format: Article
Language:English
Subjects:
Complexity dichotomy
Feedback vertex set
H-free graph
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Summary:In the Feedback Vertex Set problem, we aim to find a small set S of vertices in a graph intersecting every cycle. The Subset Feedback Vertex Set problem requires S to intersect only those cycles that include a vertex of some specified set T. We also consider the Weighted Subset Feedback Vertex Set problem, where each vertex u has weight w(u)>0 and we ask that S has small weight. By combining known NP-hardness results with new polynomial-time results we prove full complexity dichotomies for Subset Feedback Vertex Set and Weighted Subset Feedback Vertex Set for H-free graphs, that is, graphs that do not contain a graph H as an induced subgraph.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114624