Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counterexamples to the interpolating conjecture on partial-dual genus
  polynomials of ribbon graphs   Gross, Mansour and Tucker introduced the partial-dual orientable genus
polynomial and the partial-dual Euler genus polynomial. They showed that the
partial-dual genus polynomial for an orientable ribbon graph is interpolating
and gave an analogous conjecture: The partial-dual Euler-genus polynomial for
any non-orientable ribbon graph is interpolating. In this paper, we first give
some counterexamples to the conjecture. Then motivated by these
counterexamples, we further find two infinite classes of counterexamples.

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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: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: econ