Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The f-Factor Problem for Graphs and the Hereditary Property   If P is a hereditary property then we show that, for the existence of a
perfect f-factor, P is a sufficient condition for countable graphs and yields a
sufficient condition for graphs of size aleph_1. Further we give two examples
of a hereditary property which is even necessary for the existence of a perfect
f-factor. We also discuss the aleph_2-case.

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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph