Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note about monochromatic components in graphs of large minimum degree   For all positive integers $r\geq 3$ and $n$ such that $r^2-r$ divides $n$ and
an affine plane of order $r$ exists, we construct an $r$-edge colored graph
with minimum degree $(1-\frac{r-2}{r^2-r})n-2$ such that the largest
monochromatic component has order less than $\frac{n}{r-1}$. This generalizes
an example of Guggiari and Scott and, independently, Rahimi for $r=3$ and thus
disproves a conjecture of Gy\'arf\'as and S\'ark\"ozy for all integers $r\geq
3$ such that an affine plane of order $r$ exists.

12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int