Classifying Subset Feedback Vertex Set for $H$Free Graphs
Abstract
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 NPhardness results with new polynomialtime 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.00430
 Bibcode:
 2022arXiv220100430P
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Complexity;
 Computer Science  Discrete Mathematics;
 Mathematics  Combinatorics