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. (2020, December). Computing subset transversals in H-free graphs. Presented at WG 2020, Leeds, England

• Presentation Conference Type: Conference Paper (published)
• Conference Name: WG 2020
• Acceptance Date: Apr 27, 2020
• Online Publication Date: Oct 9, 2020
• Publication Date: Oct 9, 2020
• Deposit Date: Jul 12, 2020
• Publicly Available Date: Jan 21, 2021
• Print ISSN: 0302-9743
• Volume: 12301
• Pages: 187-199
• Series Title: Lecture Notes in Computer Science
• Series ISSN: 0302-9743,1611-3349
• Book Title: WG 2020: Graph-Theoretic Concepts in Computer Science
• ISBN: 9783030604394
• DOI: https://doi.org/10.1007/978-3-030-60440-0_15
• Public URL: https://durham-repository.worktribe.com/output/1140880