To decide whether a line graph (hence a claw-free graph) of maximum degree five admits a stable cutset has been proven to be an NP-complete problem. The same result has been known for K4free graphs. Here we show how to decide this problem in polynomial time for (claw, K4)-free graphs and for a claw-free graph of maximum degree at most four. As a by-product we prove that the stable cutset problem is polynomially solvable for claw-free planar graphs, and for planar line graphs. Now, the computational complexity of the stable cutset problem restricted to claw-free graphs and claw-free planar graphs is known for all bounds on the maximum degree. Moreover, we prove that the stable cutset problem remains NP-complete for K4-free planar graphs of maximum degree five. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Le, V. B., Mosca, R., & Müller, H. (2005). On stable cutsets in claw-free graphs and planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3787 LNCS, pp. 163–174). https://doi.org/10.1007/11604686_15
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