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Computational Complexity
Connected Graph
Decision Problem
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The Computational Complexity of Disconnected Cut and 2K2Partition
The Computational Complexity of Disconnected Cut and 2K2Partition,Computing Research Repository,Barnaby Martin,Daniel Paulusma
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The Computational Complexity of Disconnected Cut and 2K2Partition
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Barnaby Martin
,
Daniel Paulusma
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 NPcomplete. This problem is polynomially equivalent to the following problems: testing if a graph has a 2K2partition, testing if a graph allows a vertexsurjective homomorphism to the reflexive 4cycle 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 NPcomplete as well. This settles an open problem frequently posed in each of the four settings.
Journal:
Computing Research Repository  CORR
, vol. abs/1104.4, 2011
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