Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of Ramsey-extremal hypergraphs   In 1991, McKay and Radziszowski proved that, however each 3-subset of a
13-set is assigned one of two colours, there is some 4-subset whose four
3-subsets have the same colour. More than 25 years later, this remains the only
non-trivial classical Ramsey number known for hypergraphs. In this article, we
find all the extremal colourings of the 3-subsets of a 12-set and list some of
their properties. Using the catalogue, we provide an answer to a question of
Dudek, Fleur, Mubayi and R\"odl about the size-Ramsey numbers of hypergraphs.

35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con