Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tur\'an numbers of Berge trees   A classical conjecture of Erd\H{o}s and S\'os asks to determine the Tur\'an
number of a tree. We consider variants of this problem in the settings of
hypergraphs and multi-hypergraphs. In particular, for all $k$ and $r$, with $r
\ge k (k-2)$, we show that any $r$-uniform hypergraph $\mathcal{H}$ with more
than $\frac{n(k-1)}{r+1}$ hyperedges contains a Berge copy of any tree with $k$
edges different from the $k$-edge star. This bound is sharp when $r+1$ divides
$n$ and for such values of $n$ we determine the extremal hypergraphs.

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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
18
The categories of this paper are: econ
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The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
17
The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
1
The categories of this paper are: cs