T. Ito
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 |
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 |
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