Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple cubic graphs with no short traveling salesman tour   Let $tsp(G)$ denote the length of a shortest travelling salesman tour in a
graph $G$. We prove that for any $\varepsilon>0$, there exists a simple
$2$-connected planar cubic graph $G_1$ such that $tsp(G_1)\ge
(1.25-\varepsilon)\cdot|V(G_1)|$, a simple $2$-connected bipartite cubic graph
$G_2$ such that $tsp(G_2)\ge (1.2-\varepsilon)\cdot|V(G_2)|$, and a simple
$3$-connected cubic graph $G_3$ such that $tsp(G_3)\ge
(1.125-\varepsilon)\cdot|V(G_3)|$.

30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph