Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finding a Maximum Minimal Separator: Graph Classes and Fixed-Parameter
  Tractability   We study the problem of finding a maximum cardinality minimal separator of a
graph. This problem is known to be NP-hard even for bipartite graphs. In this
paper, we strengthen this hardness by showing that for planar bipartite graphs,
the problem remains NP-hard. Moreover, for co-bipartite graphs and for line
graphs, the problem also remains NP-hard. On the positive side, we give an
algorithm deciding whether an input graph has a minimal separator of size at
least $k$ that runs in time $2^{O(k)}n^{O(1)}$. We further show that a
subexponential parameterized algorithm does not exist unless the Exponential
Time Hypothesis (ETH) fails. Finally, we discuss a lower bound for polynomial
kernelizations of this problem.

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The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol