The computational complexity of Disconnected Cut and 2K2-Partition

Martin, B.; Paulusma, D.

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.

Citation

Martin, B., & Paulusma, D. (2011, December). The computational complexity of Disconnected Cut and 2K2-Partition. Presented at Principles and Practice of Constraint Programming, 17th International Conference, CP 2011, Perugia, Italy

• Presentation Conference Type: Conference Paper (published)
• Conference Name: Principles and Practice of Constraint Programming, 17th International Conference, CP 2011
• Publication Date: Jan 1, 2011
• Deposit Date: Dec 6, 2011
• Print ISSN: 0302-9743
• Pages: 561-575
• Series Title: Lecture notes in computer science
• Series Number: 6876
• Series ISSN: 0302-9743,1611-3349
• Book Title: Principles and practice of constraint programming, 17th International Conference, CP 2011, 12-16 September 2011, Perugia, Italy ; proceedings.
• ISBN: 9783642237850
• DOI: https://doi.org/10.1007/978-3-642-23786-7_43
• Public URL: https://durham-repository.worktribe.com/output/1158287