Computing weighted subset odd cycle transversals in H-free graphs

Brettell, N.; Johnson, M.; Paulusma, D.

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 almost-complete complexity dichotomy for Weighted Subset Odd Cycle Transversal for graphs that do not contain a graph H as an induced subgraph. In particular, our result shows that the complexities of the weighted and unweighted variant do not align on H-free graphs, just as Papadopoulos and Tzimas showed for Subset Feedback Vertex Set.

• Journal Article Type: Article
• Acceptance Date: Mar 21, 2022
• Online Publication Date: Apr 8, 2022
• Publication Date: 2022-09
• Deposit Date: May 18, 2022
• Publicly Available Date: Apr 8, 2023
• Journal: Journal of Computer and System Sciences
• Print ISSN: 0022-0000
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 128
• Pages: 71-85
• DOI: https://doi.org/10.1016/j.jcss.2022.03.002
• Public URL: https://durham-repository.worktribe.com/output/1207719