The Computational Complexity of Disconnected Cut and 2K2-Partition

Barnaby Martin; Daniel Paulusma

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arXiv · 1104.4779

The Computational Complexity of Disconnected Cut and 2K2-Partition

Barnaby Martin·Daniel Paulusma

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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.

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Barnaby Martin, Daniel Paulusma. 2011-04-25. The Computational Complexity of Disconnected Cut and 2K2-Partition. https://arxiv.org/abs/1104.4779

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