Abstract
We study the computational complexity of finding a maximum independent set of vertices in a planar graph. In general, this problem is known to be NP-hard. However, under certain restrictions it becomes polynomial-time solvable. We identify a graph parameter to which the complexity of the problem is sensible and produce a number of both negative (intractable) and positive (solvable in polynomial time) results, generalizing several known facts.
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Alekseev, V.E., Lozin, V., Malyshev, D., Milanič, M. (2008). The Maximum Independent Set Problem in Planar Graphs. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_7
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DOI: https://doi.org/10.1007/978-3-540-85238-4_7
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