Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connected tree-width   The connected tree-width of a graph is the minimum width of a
tree-decomposition whose parts induce connected subgraphs. Long cycles are
examples of graphs that have small tree-width but large connected tree-width.
We show that a graph has small connected tree-width if and only if it has small
tree-width and contains no long geodesic cycle.
  We further prove a connected analogue of the duality theorem for tree-width:
a finite graph has small connected tree-width if and only if it has no bramble
whose connected covers are all large. Both these results are qualitative: the
bounds are good but not tight.
  We show that graphs of connected tree-width $k$ are $k$-hyperbolic, which is
tight, and that graphs of tree-width $k$ whose geodesic cycles all have length
at most $\ell$ are $\lfloor{3\over2}\ell(k-1)\rfloor$-hyperbolic. The existence
of such a function $h(k,\ell)$ had been conjectured by Sullivan.

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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys