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On stable cutsets in claw-free graphs and planar graphs

Bang Le, V., Mosca, R. and Muller, H. (2008) On stable cutsets in claw-free graphs and planar graphs. Journal of Discrete Algorithms, 6 (2). pp. 256-276. ISSN 1570-8667

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A stable cutset in a connected graph is a stable set whose deletion disconnects the graph. Let K4 and K1,3 (claw) denote the complete (bipartite) graph on 4 and 1+3 vertices. It is NP-complete to decide whether a line graph (hence a claw-free graph) with maximum degree five or a K4-free graph admits a stable cutset. Here we describe algorithms deciding in polynomial time whether a claw-free graph with maximum degree at most four or whether a (claw, K4)-free graph admits a stable cutset. As a by-product we obtain that the stable cutset problem is polynomially solvable for claw-free planar graphs, and also for planar line graphs. Thus, the computational complexity of the stable cutset problem is completely determined for claw-free graphs with respect to degree constraint, and for claw-free planar graphs. Moreover, we prove that the stable cutset problem remains NP-complete for K4-free planar graphs with maximum degree five.

Item Type: Article
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Sherpa Assistant
Date Deposited: 04 Sep 2008 14:10
Last Modified: 18 Jun 2015 17:26
Published Version: http://dx.doi.org/10.1016/j.jda.2007.04.001
Status: Published
Publisher: Elsevier B.V.
Identification Number: 10.1016/j.jda.2007.04.001
URI: http://eprints.whiterose.ac.uk/id/eprint/4607

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