Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On globally sparse Ramsey graphs   We say that a graph $G$ has the Ramsey property w.r.t.\ some graph $F$ and
some integer $r\geq 2$, or $G$ is $(F,r)$-Ramsey for short, if any $r$-coloring
of the edges of $G$ contains a monochromatic copy of $F$. R{\"o}dl and
Ruci{\'n}ski asked how globally sparse $(F,r)$-Ramsey graphs $G$ can possibly
be, where the density of $G$ is measured by the subgraph $H\subseteq G$ with
the highest average degree. So far, this so-called Ramsey density is known only
for cliques and some trivial graphs $F$. In this work we determine the Ramsey
density up to some small error terms for several cases when $F$ is a complete
bipartite graph, a cycle or a path, and $r\geq 2$ colors are available.

26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph