Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal $3$-wise intersecting families   A family $\mathcal{F}$ of subsets of $\{1,2,\ldots,n\}$ is called maximal
$k$-wise intersecting if every collection of at most $k$ members from
$\mathcal{F}$ has a common element, and moreover no set can be added to
$\mathcal{F}$ while preserving this property. In 1974, Erd\H{o}s and Kleitman
asked for the smallest possible size of a maximal $k$-wise intersecting family,
for $k\ge 3$. We resolve this problem for $k=3$ and $n$ even and sufficiently
large.

32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: chem-ph