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arXiv · 1304.6189

On the parameterized complexity of cutting a few vertices from a graph

Fedor V. Fomin·Petr A. Golovach·Janne H. Korhonen
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Abstract

We study the parameterized complexity of separating a small set of vertices from a graph by a small vertex-separator. That is, given a graph $G$ and integers $k$, $t$, the task is to find a vertex set $X$ with $|X| \le k$ and $|N(X)| \le t$. We show that - the problem is fixed-parameter tractable (FPT) when parameterized by $t$ but W[1]-hard when parameterized by $k$, and - a terminal variant of the problem, where $X$ must contain a given vertex $s$, is W[1]-hard when parameterized either by $k$ or by $t$ alone, but is FPT when parameterized by $k + t$. We also show that if we consider edge cuts instead of vertex cuts, the terminal variant is NP-hard.

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Fedor V. Fomin, Petr A. Golovach, Janne H. Korhonen. 2013-10-01. On the parameterized complexity of cutting a few vertices from a graph. https://doi.org/10.1007/978-3-642-40313-2_38

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