Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal problems related to Betti numbers of flag complexes   We study the problem of maximizing Betti numbers of simplicial complexes. We
prove an upper bound of 1.32^n for the sum of Betti numbers of any n-vertex
flag complex and 1.25^n for the independence complex of a triangle-free graph.
These findings imply upper bounds for the Betti numbers of various related
classes of spaces, including the neighbourhood complex of a graph. We also make
some related observations.

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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph