Given an undirected graph with weights on its vertices, the k most vital nodes independent set problem consists of determining a set of k vertices whose removal results in the greatest decrease in the maximum weight of independent sets. We also consider the complementary problem, minimum node blocker independent set that consists of removing a subset of vertices of minimum size such that the maximum weight of independent sets in the remaining graph is at most a specified value. We show that these problems are NP-hard on bipartite graphs but polynomial-time solvable on unweighted bipartite graphs. Furthermore, these problems are polynomial also on graphs of bounded treewidth and cographs. A result on the non-existence of a ptas is presented, too. © 2011 Springer-Verlag.
CITATION STYLE
Bazgan, C., Toubaline, S., & Tuza, Z. (2011). Complexity of most vital nodes for independent set in graphs related to tree structures. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6460 LNCS, pp. 154–166). Springer Verlag. https://doi.org/10.1007/978-3-642-19222-7_17
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