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 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