Computing subset transversals in H-free graphs

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

Abstract

we study the computational complexity of two well-known graph transversal problems, namely Subset Feedback Vertex Set and Subset Odd Cycle Transversal, by restricting the input to H-free graphs, that is, to graphs that do not contain some fixed graph H as an induced subgraph. By combining known and new results, we determine the computational complexity of both problems on H-free graphs for every graph H except when H = sP1 + P4 for some s ≥ 1. As part of our approach, we introduce the Subset Vertex Cover problem and prove that it is polynomial-time solvable for (sP1 + P4)-free graphs for every s ≥ 1

Citation

Brettell, N., Johnson, M., Paesani, G., & Paulusma, D. (2022). Computing subset transversals in H-free graphs. Theoretical Computer Science, 902, 76-92. https://doi.org/10.1016/j.tcs.2021.12.010

• Journal Article Type: Article
• Acceptance Date: Dec 17, 2021
• Online Publication Date: Dec 21, 2021
• Publication Date: Jan 18, 2022
• Deposit Date: Dec 31, 2021
• Publicly Available Date: Dec 21, 2022
• Journal: Theoretical Computer Science
• Print ISSN: 0304-3975
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 902
• Pages: 76-92
• DOI: https://doi.org/10.1016/j.tcs.2021.12.010
• Public URL: https://durham-repository.worktribe.com/output/1221498