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

Martin, Barnaby and Paulusma, Daniël
(2011)
*The computational complexity of disconnected cut and 2K2-partition.*
In: The 17th International Conference on Principles and Practice of Constraint Programming (CP 2011), 12-16 Sep 2011, Perugia, Italy.
(doi:10.1007/978-3-642-23786-7_43)

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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.

Item Type: | Conference or Workshop Item (Paper) |
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Additional Information: | Martin B., Paulusma D. (2011) The Computational Complexity of Disconnected Cut and 2K2-Partition. In: Lee J. (eds) Principles and Practice of Constraint Programming – CP 2011. CP 2011. Lecture Notes in Computer Science, vol 6876. Springer, Berlin, Heidelberg |

Research Areas: | A. > School of Science and Technology > Computer Science A. > School of Science and Technology > Computer Science > Foundations of Computing group |

Item ID: | 9674 |

Useful Links: | |

Depositing User: | Devika Mohan |

Date Deposited: | 14 Jan 2013 10:17 |

Last Modified: | 24 Apr 2018 15:10 |

ISBN: | 9783642237850 |

URI: | https://eprints.mdx.ac.uk/id/eprint/9674 |

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