Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finding Maximal Sets of Laminar 3-Separators in Planar Graphs in Linear
  Time   We consider decomposing a 3-connected planar graph $G$ using laminar
separators of size three. We show how to find a maximal set of laminar
3-separators in such a graph in linear time. We also discuss how to find
maximal laminar set of 3-separators from special families. For example we
discuss non-trivial cuts, ie. cuts which split $G$ into two components of size
at least two. For any vertex $v$, we also show how to find a maximal set of
3-separators disjoint from $v$ which are laminar and satisfy: every vertex in a
separator $X$ has two neighbours not in the unique component of $G-X$
containing $v$. In all cases, we show how to construct a corresponding tree
decomposition of adhesion three. Our new algorithms form an important component
of recent methods for finding disjoint paths in nonplanar graphs.

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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio