Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Negative (and Positive) Circles in Signed Graphs: A Problem Collection   A signed graph is a graph whose edges are labelled positive or negative. The
sign of a circle (cycle, circuit) is the product of the signs of its edges.
Most of the essential properties of a signed graph depend on the signs of its
circles. Here I describe several questions regarding negative circles and their
cousins the positive circles. Topics include incidence between signed circles
and edges or vertices, characterizing signed graphs with special circle
properties, counting negative circles, signed-circle packing and covering,
signed circles and eigenvalues, and directed cycles in signed digraphs. A few
of the questions come with answers.

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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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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: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc