Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Preventing Small $\mathbf{(s,t)}$-Cuts by Protecting Edges   We introduce and study Weighted Min $(s,t)$-Cut Prevention, where we are
given a graph $G=(V,E)$ with vertices $s$ and $t$ and an edge cost function and
the aim is to choose an edge set $D$ of total cost at most $d$ such that $G$
has no $(s,t)$-edge cut of capacity at most $a$ that is disjoint from $D$. We
show that Weighted Min $(s,t)$-Cut Prevention is NP-hard even on subcubcic
graphs when all edges have capacity and cost one and provide a comprehensive
study of the parameterized complexity of the problem. We show, for example
W[1]-hardness with respect to $d$ and an FPT algorithm for $a$.

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The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn