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 kn...

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Bibliographic Details
Published in:arXiv.org 2021-10
Main Authors: Brettell, Nick, Johnson, Matthew, Paesani, Giacomo, Paulusma, Daniël
Format: Article
Language:English
Subjects:
Complexity
Graph theory
Graphs
Polynomials
Online Access:Get full text
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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 \(H=sP_1+P_4\) for some \(s\geq 1\). As part of our approach, we introduce the Subset Vertex Cover problem and prove that it is polynomial-time solvable for \((sP_1+P_4)\)-free graphs for every \(s\geq 1\).
ISSN:2331-8422