Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: k --Universal Finite Graphs   This paper investigates the class of k-universal finite graphs, a local
analog of the class of universal graphs, which arises naturally in the study of
finite variable logics. The main results of the paper, which are due to Shelah,
establish that the class of k-universal graphs is not definable by an infinite
disjunction of first-order existential sentences with a finite number of
variables and that there exist k-universal graphs with no k-extendible induced
subgraphs.

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The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th