On disconnected cuts and separators

Ito, T.; Kaminski, M.; Paulusma, D.; Thilikos, D.M.

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. A natural condition is to impose that for any u∈U, the subgraph induced by (V∖U)∪{u} is connected. In that case, U is called a minimal disconnected cut. We show that the problem of testing whether a graph has a minimal disconnected cut is NP-complete. We also show that the problem of testing whether a graph has a disconnected cut separating two specified vertices, s and t, is NP-complete.

Citation

Ito, T., Kaminski, M., Paulusma, D., & Thilikos, D. (2011). On disconnected cuts and separators. Discrete Applied Mathematics, 159(13), 1345-1351. https://doi.org/10.1016/j.dam.2011.04.027

• Journal Article Type: Article
• Publication Date: Aug 1, 2011
• Deposit Date: Dec 6, 2011
• Journal: Discrete Applied Mathematics
• Print ISSN: 0166-218X
• Electronic ISSN: 1872-6771
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 159
• Issue: 13
• Pages: 1345-1351
• DOI: https://doi.org/10.1016/j.dam.2011.04.027
• Keywords: Cut set, 2K2-partition, Retraction, Compaction.
• Public URL: https://durham-repository.worktribe.com/output/1533525