In the Feedback Vertex Set problem, we aim to find a small set S of vertices in a graph intersecting every cycle. The Subset 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 for Subset Feedback Vertex Set and Weighted Subset Feedback Vertex Set for H-free graphs, that is, graphs that do not contain a graph H as an induced subgraph.
@article{arxiv.2201.00430,
title = {Classifying Subset Feedback Vertex Set for $H$-Free Graphs},
author = {Giacomo Paesani and Daniël Paulusma and Paweł Rzążewski},
journal= {arXiv preprint arXiv:2201.00430},
year = {2022}
}