Minimal Disconnected Cuts in Planar Graphs

Kamiński, M.; Paulusma, D.; Stewart, A.; Thilikos, D.

doi:10.1002/net.21696

Minimal Disconnected Cuts in Planar Graphs

Kamiński, M.; Paulusma, D.; Stewart, A.; Thilikos, D.

Authors

M. Kamiński

Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor

A. Stewart

D. Thilikos

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.

Citation

Kamiński, M., Paulusma, D., Stewart, A., & Thilikos, D. (2016). Minimal Disconnected Cuts in Planar Graphs. Networks, 68(4), 250-259. https://doi.org/10.1002/net.21696

Journal Article Type	Article
Acceptance Date	Jul 26, 2016
Online Publication Date	Aug 8, 2016
Publication Date	Dec 1, 2016
Deposit Date	Oct 1, 2016
Publicly Available Date	Aug 8, 2017
Journal	Networks
Print ISSN	0028-3045
Electronic ISSN	1097-0037
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	68
Issue	4
Pages	250-259
DOI	https://doi.org/10.1002/net.21696
Public URL	https://durham-repository.worktribe.com/output/1403689

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Copyright 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.