Elsevier

Discrete Applied Mathematics

Volume 251, 31 December 2018, Pages 334-339
Discrete Applied Mathematics

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Defensive alliances in graphs of bounded treewidth

https://doi.org/10.1016/j.dam.2018.04.001Get rights and content
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Abstract

The Defensive Alliance problem has been studied extensively during the last fifteen years, but the question whether it is FPT when parameterized by treewidth has still remained open. We show that this problem is W[1]-hard. This puts it among the few problems that are FPT when parameterized by solution size but not when parameterized by treewidth (unless FPT=W[1]).

Keywords

Defensive alliance
Treewidth
Parameterized complexity

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