Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

Minimal disconnected cuts in planar graphs.

Kamiński, M. and Paulusma, D. and Stewart, A. and Thilikos, D. (2016) 'Minimal disconnected cuts in planar graphs.', Networks., 68 (4). pp. 250-259.

Abstract

The problem of finding a disconnected cut in a graph is NP-hard in general but polynomial-time solvable on planar graphs. The problem of finding a minimal disconnected cut is also NP-hard but its computational complexity was not known for planar graphs. We show that it is polynomial-time solvable on 3-connected planar graphs but NP-hard for 2-connected planar graphs. Our technique for the first result is based on a structural characterization of minimal disconnected cuts in 3-connected inline image-free-minor graphs and on solving a topological minor problem in the dual. In addition we show that the problem of finding a minimal connected cut of size at least 3 is NP-hard for 2-connected apex graphs. Finally, we relax the notion of minimality and prove that the problem of finding a so-called semi-minimal disconnected cut is still polynomial-time solvable on planar graphs.

Item Type:Article
Full text:(AM) Accepted Manuscript
Download PDF
(340Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1002/net.21696
Publisher statement:This is the accepted version of the following article: Kamiński, M., Paulusma, D., Stewart, A. and Thilikos, D. M. (2016), Minimal disconnected cuts in planar graphs. Networks. 68(4): 250-259, which has been published in final form at http://dx.doi.org/10.1002/net.21696. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
Date accepted:26 July 2016
Date deposited:03 October 2016
Date of first online publication:08 August 2016
Date first made open access:08 August 2017

Save or Share this output

Export:
Export
Look up in GoogleScholar