# Computing Weighted Subset Transversals in $H$-Free Graphs

28 Jul 2020  ·  Nick Brettell, Matthew Johnson, Daniel Paulusma ·

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 almost-complete 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.

PDF Abstract

## Code Add Remove Mark official

No code implementations yet. Submit your code now

## Categories

Data Structures and Algorithms Discrete Mathematics Combinatorics

## Datasets

Add Datasets introduced or used in this paper