Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regular Tur\'an numbers   The regular Tur\'an number of a graph $F$, denoted by rex$(n,F)$, is the
largest number of edges in a regular graph $G$ of order $n$ such that $G$ does
not contain subgraphs isomorphic to $F$. Giving a partial answer to a recent
problem raised by Gerbner et al. [arXiv:1909.04980] we prove that rex$(n,F)$
asymptotically equals the (classical) Tur\'an number whenever the chromatic
number of $F$ is at least four; but it is substantially different for some
3-chromatic graphs $F$ if $n$ is odd.

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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an