Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite planar emulators for K_{4,5} - 4K_2 and K_{1,2,2,2} and Fellows'
  Conjecture   In 1988 Fellows conjectured that if a finite, connected graph admits a finite
planar emulator, then it admits a finite planar cover. We construct a finite
planar emulator for K_{4,5} - 4K_2. Archdeacon showed that K_{4,5} - 4K_2 does
not admit a finite planar cover; thus K_{4,5} - 4K_2 provides a counterexample
to Fellows' Conjecture.
  It is known that Negami's Planar Cover Conjecture is true if and only if
K_{1,2,2,2} admits no finite planar cover. We construct a finite planar
emulator for K_{1,2,2,2}. The existence of a finite planar cover for
K_{1,2,2,2} is still open.

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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn