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The computational complexity of disconnected cut and 2K2-partition.

Martin, B. and Paulusma, D. (2015) 'The computational complexity of disconnected cut and 2K2-partition.', Journal of combinatorial theory, series B., 111 . pp. 17-37.

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.

Item Type:Article
Keywords:Graph theory, Disconnected cut, 2K2-partition, Biclique cover.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.jctb.2014.09.002
Publisher 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
Date accepted:No date available
Date deposited:08 January 2015
Date of first online publication:26 September 2014
Date first made open access:26 March 2016

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