The Computational Complexity of Disconnected Cut and 2K2-Partition

  • Barnaby Martin
  • Daniël Paulusma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6876)


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 2K 2-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.


Computational Complexity Constraint Satisfaction Input Graph Surjective Homomorphism Span Subgraph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Barnaby Martin
    • 1
  • Daniël Paulusma
    • 1
  1. 1.School of Engineering and Computing SciencesDurham University, Science LaboratoriesDurhamUnited Kingdom

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