Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ordered Size Ramsey Number of Paths   An ordered graph is a simple graph with an ordering on its vertices. Define
the ordered path $P_n$ to be the monotone increasing path with $n$ edges. The
ordered size Ramsey number $\tilde{r}(P_r,P_s)$ is the minimum number $m$ for
which there exists an ordered graph $H$ with $m$ edges such that every
two-coloring of the edges of $H$ contains a red copy of $P_r$ or a blue copy of
$P_s$. For $2\leq r\leq s$, we show $\frac{1}{8}r^2s\leq \tilde{r}(P_r,P_s)\leq
Cr^2s(\log s)^3$, where $C>0$ is an absolute constant. This problem is
motivated by the recent results of Buci\'c-Letzter-Sudakov and Letzter-Sudakov
for oriented graphs.

23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga