Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new bound for the cops and robbers problem   In this short paper we study the game of cops and robbers, which is played on
the vertices of some fixed graph $G$. Cops and a robber are allowed to move
along the edges of $G$ and the goal of cops is to capture the robber. The cop
number $c(G)$ of $G$ is the minimum number of cops required to win the game.
Meyniel conjectured a long time ago that $O(\sqrt{n})$ cops are enough for any
connected $G$ on $n$ vertices. Improving several previous results, we prove
that the cop number of $n$-vertex graph is at most $n 2^{-(1+o(1))\sqrt{\log
n}}$.

22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
18
The categories of this paper are: econ
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat