Computing weighted subset transversals in H-free graphs

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

Abstract

For the Odd Cycle Transversal problem, the task is to nd a small set S of vertices in a graph that intersects every cycle of odd length. The Subset Odd Cycle Transversal 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.

Citation

Brettell, N., Johnson, M., & Paulusma, D. (2021, August). Computing weighted subset transversals in H-free graphs. Presented at WADS 2021, Halifax, Nova Scotia

• Presentation Conference Type: Conference Paper (published)
• Conference Name: WADS 2021
• Start Date: Aug 9, 2021
• End Date: Aug 11, 2021
• Acceptance Date: Apr 13, 2021
• Online Publication Date: Jul 31, 2021
• Publication Date: 2021
• Deposit Date: May 28, 2021
• Publicly Available Date: Jun 1, 2021
• Print ISSN: 0302-9743
• Publisher: Springer Verlag
• Pages: 229-242
• Series Title: Lecture Notes in Computer Science
• Series Number: 12808
• Series ISSN: 0302-9743
• Book Title: Algorithms and Data Structures 17th International Symposium, WADS 2021, Virtual Event, August 9–11, 2021, Proceedings
• ISBN: 978-3-030-83507-1
• DOI: https://doi.org/10.1007/978-3-030-83508-8_17
• Public URL: https://durham-repository.worktribe.com/output/1139387