Computing Weighted Subset Transversals in H-Free Graphs

For the Odd Cycle Transversal problem, task is to find a small set S of vertices in graph that intersects every cycle odd length. The Subset requires intersect only those cycles include vertex distinguished subset T. If we are given weights for vertices, ask instead has weight: this problem Weighted Transversal. We prove an almost-complete complexity dichotomy graphs do not contain H as induced subgraph. Our general approach can also be used Feedback Vertex Set, which enables us generalize recent result Papadopoulos and Tzimas.