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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.

Minimum connected transversals in graphs: New hardness results and tractable cases using the price of connectivity Thumbnail


Authors

N. Chiarelli

T.R. Hartinger

M. Johnson

M. Milanič



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 Mar 28, 2024
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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