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The Computational Complexity of Disconnected Cut and 2K2-Partition

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

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 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.

Keywords

Computational Complexity Constraint Satisfaction Input Graph Surjective Homomorphism Span Subgraph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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