Abstract
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 \(s\ge 1\). 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 \(s\ge 1\).
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