# Classifying Subset Feedback Vertex Set for H-Free Graphs

@article{Paesani2022ClassifyingSF, title={Classifying Subset Feedback Vertex Set for H-Free Graphs}, author={Giacomo Paesani and Dani{\"e}l Paulusma and Paweł Rzaͅżewski}, journal={ArXiv}, year={2022}, volume={abs/2201.00430} }

. In the Feedback Vertex Set problem, we aim to ﬁnd a small set S of vertices in a graph intersecting every cycle. The Sub- set 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…

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