Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Tur\'an density of $\{1, 3\}$-Hypergraphs   In this paper, we consider the Tur\'an problems on $\{1,3\}$-hypergraphs. We
prove that a $\{1, 3\}$-hypergraph is degenerate if and only if it's $H^{\{1,
3\}}_5$-colorable, where $H^{\{1, 3\}}_5$ is a hypergraph with vertex set
$V=[5]$ and edge set $E=\{\{2\}, \{3\}, \{1, 2, 4\}, \{1, 3, 5\}, \{1, 4,
5\}\}.$ Using this result, we further prove that for any finite set $R$ of
distinct positive integers, except the case $R=\{1, 2\}$, there always exist
non-trivial degenerate $R$-graphs. We also compute the Tur\'an densities of
some small $\{1,3\}$-hypergraphs.

28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex