Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-branching tree-decompositions   We prove that if a graph has a tree-decomposition of width at most w, then it
has a tree-decomposition of width at most w with certain desirable properties.
We will use this result in a subsequent paper to show that every 2-connected
graph of large path-width has a minor isomorphic to either a large tree with a
vertex attached to every vertex of the tree or a large outerplanar graph.

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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: physics
4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin