Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the existence of an alternating sign on a spanning tree of
  graphs   For a spanning tree T of a connected graph G and for a labelling \phi: E(T)
\rightarrow {+, -}, \phi is called an alternating sign on a spanning tree T of
a graph G if for any cotree edge e \in E(G)-E(T), the unique path in T joining
both end vertices of e has alternating signs. In the present note, we prove
that any graph has a spanning tree T and an alternating sign on T.

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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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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: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: econ