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- W4386880079 abstract "The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. Such a problem is $$textsf{NP}$$ -complete even when the input graph is planar and has maximum degree five. In this paper, we first present a $$mathcal {O}^*(1.4423^{n})$$ -time algorithm to compute a minimum independent cutset (if any). Since the property of having an independent cutset is MSO $$_1$$ -expressible, our main results are concerned with structural parameterizations for the problem considering parameters incomparable with clique-width. We present $$textsf{FPT}$$ -time algorithms for the problem considering the following parameters: the dual of the maximum degree, the dual of the solution size, the size of a dominating set (where a dominating set is given as an additional input), the size of an odd cycle transversal, the distance to chordal graphs, and the distance to $$P_5$$ -free graphs. We close by introducing the notion of $$alpha $$ -domination, which allows us to identify more fixed-parameter tractable and polynomial-time solvable cases." @default.
- W4386880079 created "2023-09-21" @default.
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- W4386880079 date "2023-01-01" @default.
- W4386880079 modified "2023-09-27" @default.
- W4386880079 title "Exact and Parameterized Algorithms for the Independent Cutset Problem" @default.
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- W4386880079 doi "https://doi.org/10.1007/978-3-031-43587-4_27" @default.
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