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Minimal disconnected cuts in planar graphs.

Kamiński, M. and Paulusma, D. and Stewart, A. and Thilikos, D.M. (2015) 'Minimal disconnected cuts in planar graphs.', in Fundamentals of computation theory : 20th International Symposium, FCT 2015, Gdańsk, Poland, August 17-19, 2015, proceedings. , pp. 243-254. Lecture notes in computer science. (9210).


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 is 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 K 3,3 -free-minor graphs and on solving a topological minor problem in the dual. We show that the latter problem can be solved in polynomial-time even on general graphs. 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.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:21 August 2015
Date of first online publication:August 2015
Date first made open access:04 August 2016

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