Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lengths of edges in carrier graphs   We show that if X is a minimal length carrier graph in a hyperbolic
3-manifold, M, then if X contains a sufficiently short edge, it must contain a
short circuit, as well. The meaning of "short" depends only on the rank of the
fundamental group of M. We also expand the class of manifolds which are known
to have minimal length carrier graphs.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: physics