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.

Computing subset transversals in H-free graphs / Brettell, N.; Johnson, M.; Paesani, G.; Paulusma, D.. - In: THEORETICAL COMPUTER SCIENCE. - ISSN 0304-3975. - 902:(2022), pp. 76-92. [10.1016/j.tcs.2021.12.010]

Computing subset transversals in H-free graphs

Paesani G.;
2022

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.
2022
Complexity dichotomy; Feedback vertex; H-free; Hereditary graph class; Odd cycle transversal
01 Pubblicazione su rivista::01a Articolo in rivista
Computing subset transversals in H-free graphs / Brettell, N.; Johnson, M.; Paesani, G.; Paulusma, D.. - In: THEORETICAL COMPUTER SCIENCE. - ISSN 0304-3975. - 902:(2022), pp. 76-92. [10.1016/j.tcs.2021.12.010]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1747527
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