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Computing subset transversals in H-free graphs

Brettell, N. and Johnson, M. and Paesani, G. and Paulusma, D. (2020) 'Computing subset transversals in H-free graphs.', in WG 2020: Graph-Theoretic Concepts in Computer Science. , pp. 187-199. Lecture Notes in Computer Science., 12301

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 .

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/978-3-030-60440-0_15
Publisher statement:The final authenticated version is available online at https://doi.org/10.1007/978-3-030-60440-0_15
Date accepted:27 April 2020
Date deposited:21 January 2021
Date of first online publication:09 October 2020
Date first made open access:21 January 2021

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