19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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The Computational Complexity of Disconnected Cut and 2K2-Partition

Presented by Dr. Barnaby MARTIN
Type: Oral presentation
Track: Algorithmic Graph Theory


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.


Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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