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

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.14514
 Bibcode:
 2020arXiv200714514B
 Keywords:

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