The Computational Complexity of Disconnected Cut and 2K2-Partition
Abstract
For a connected graph G=(V,E), a subset U of 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.
Cite
@article{arxiv.1104.4779,
title = {The Computational Complexity of Disconnected Cut and 2K2-Partition},
author = {Barnaby Martin and Daniel Paulusma},
journal= {arXiv preprint arXiv:1104.4779},
year = {2014}
}
Comments
Conference version appeared at CP 2011. To appear JCTB (DOI: 10.1016/j.jctb.2014.09.002)