Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved lower bound on an Euclidean Ramsey problem   It was previously shown that any two-colour colouring of K(C_n) must contain
a monochromatic planar K_4 subgraph for n >= N^*, where 6 <= N^* <= N and N is
Graham's number. The bound was later improved to 11 <= N^* <= N. In this
article, it is improved to 13 <= N^* <= N.

8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph