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The computational complexity of disconnected cut and 2K2-partition

Martin, B.; Paulusma, D.

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Abstract

For a connected graph G=(V,E), a subset U⊆V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. We show that the problem to test whether a graph has a disconnected cut is NP-complete. This problem is polynomially equivalent to the following problems: testing if a graph has a 2K2-partition, testing if a graph allows a vertex-surjective homomorphism to the reflexive 4-cycle and testing if a graph has a spanning subgraph that consists of at most two bicliques. Hence, as an immediate consequence, these three decision problems are NP-complete as well. This settles an open problem frequently posed in each of the four settings.

Citation

Martin, B., & Paulusma, D. (2015). The computational complexity of disconnected cut and 2K2-partition. Journal of Combinatorial Theory, Series B, 111, 17-37. https://doi.org/10.1016/j.jctb.2014.09.002

Journal Article Type Article
Online Publication Date Sep 26, 2014
Publication Date Mar 1, 2015
Deposit Date Dec 20, 2014
Publicly Available Date Mar 28, 2024
Journal Journal of Combinatorial Theory, Series B
Print ISSN 0095-8956
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 111
Pages 17-37
DOI https://doi.org/10.1016/j.jctb.2014.09.002
Keywords Graph theory, Disconnected cut, 2K2-partition, Biclique cover.
Public URL https://durham-repository.worktribe.com/output/1415061

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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of combinatorial theory, Series B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of combinatorial theory, Series B, 111, March 2015, 10.1016/j.jctb.2014.09.002





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