We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

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.


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
Download PDF
Publisher Web site:
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

Save or Share this output

Look up in GoogleScholar