N. Chiarelli
Minimum connected transversals in graphs: New hardness results and tractable cases using the price of connectivity
Chiarelli, N.; Hartinger, T.R.; Johnson, M.; Milanič, M.; Paulusma, D.
Authors
T.R. Hartinger
M. Johnson
M. Milanič
Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor
Abstract
We perform a systematic study in the computational complexity of the connected variant of three related transversal problems: Vertex Cover, Feedback Vertex Set, and Odd Cycle Transversal. Just like their original counterparts, these variants are NP-complete for general graphs. A graph G is H-free for some graph H if G contains no induced subgraph isomorphic to H. It is known that Connected Vertex Cover is NP-complete even for H-free graphs if H contains a claw or a cycle. We show that the two other connected variants also remain NP-complete if H contains a cycle or claw. In the remaining case H is a linear forest. We show that Connected Vertex Cover, Connected Feedback Vertex Set, and Connected Odd Cycle Transversal are polynomial-time solvable for sP2-free graphs for every constant s≥1. For proving these results we use known results on the price of connectivity for vertex cover, feedback vertex set, and odd cycle transversal. This is the first application of the price of connectivity that results in polynomial-time algorithms.
Citation
Chiarelli, N., Hartinger, T., Johnson, M., Milanič, M., & Paulusma, D. (2018). Minimum connected transversals in graphs: New hardness results and tractable cases using the price of connectivity. Theoretical Computer Science, 705, 75-83. https://doi.org/10.1016/j.tcs.2017.09.033
Journal Article Type | Article |
---|---|
Acceptance Date | Sep 27, 2017 |
Online Publication Date | Oct 4, 2017 |
Publication Date | Jan 1, 2018 |
Deposit Date | Oct 18, 2017 |
Publicly Available Date | Oct 4, 2018 |
Journal | Theoretical Computer Science |
Print ISSN | 0304-3975 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 705 |
Pages | 75-83 |
DOI | https://doi.org/10.1016/j.tcs.2017.09.033 |
Public URL | https://durham-repository.worktribe.com/output/1373588 |
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Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright Statement
© 2017 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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